diff --git a/README.md b/README.md
index e3c3bfa..7b30636 100644
--- a/README.md
+++ b/README.md
@@ -550,6 +550,19 @@ Highly experimental personal projects.
         * [Fermat pseudoprimes of the form p*((p-1)*n + 1)](./oeis-research/Daniel%20Suteu/Fermat%20pseudoprimes%20of%20the%20form%20p*((p-1)*n%20+%201))
             * [prog.pl](./oeis-research/Daniel%20Suteu/Fermat%20pseudoprimes%20of%20the%20form%20p*((p-1)*n%20+%201)/prog.pl)
             * [prog.sf](./oeis-research/Daniel%20Suteu/Fermat%20pseudoprimes%20of%20the%20form%20p*((p-1)*n%20+%201)/prog.sf)
+        * [First number k such that k + a(i) has n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
+            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
+        * [First number k such that k + a(i) is the product of n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20is%20the%20product%20of%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
+            * [prog.pl](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20is%20the%20product%20of%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.pl)
+            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20k%20+%20a(i)%20is%20the%20product%20of%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
+        * [First number k such that the concatenation of a(i) and k has n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
+            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
+        * [First number k such that the concatenation of a(i) and k has n prime factors, counted with multiplicity, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n)
+            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20a(i)%20and%20k%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/prog.sf)
+        * [First number k such that the concatenation of k and a(i) has n distinct prime factors, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n)
+            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20distinct%20prime%20factors,%20for%20all%20i%20<%20n/prog.sf)
+        * [First number k such that the concatenation of k and a(i) has n prime factors, counted with multiplicity, for all i < n](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n)
+            * [prog.sf](./oeis-research/Daniel%20Suteu/First%20number%20k%20such%20that%20the%20concatenation%20of%20k%20and%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/prog.sf)
         * [Generalized class of primes](./oeis-research/Daniel%20Suteu/Generalized%20class%20of%20primes)
             * [prog.sf](./oeis-research/Daniel%20Suteu/Generalized%20class%20of%20primes/prog.sf)
         * [Incrementally largest numbers n that are the product of primes p such that p+1 divides n](./oeis-research/Daniel%20Suteu/Incrementally%20largest%20numbers%20n%20that%20are%20the%20product%20of%20primes%20p%20such%20that%20p+1%20divides%20n)
@@ -1080,6 +1093,8 @@ Highly experimental personal projects.
             * [is squarefree omega prime.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%204%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_omega_prime.sf)
         * [Least prime p such that p^n + 6 is the product of n distinct primes](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%206%20is%20the%20product%20of%20n%20distinct%20primes)
             * [is squarefree almost prime.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Least%20prime%20p%20such%20that%20p^n%20+%206%20is%20the%20product%20of%20n%20distinct%20primes/is_squarefree_almost_prime.sf)
+        * [Smallest k such that 3^(4*3^n) - k is a safe prime](./oeis-research/J.W.L.%20(Jan)%20Eerland/Smallest%20k%20such%20that%203^(4*3^n)%20-%20k%20is%20a%20safe%20prime)
+            * [prog.sf](./oeis-research/J.W.L.%20(Jan)%20Eerland/Smallest%20k%20such%20that%203^(4*3^n)%20-%20k%20is%20a%20safe%20prime/prog.sf)
     * [Jacques Tramu](./oeis-research/Jacques%20Tramu)
         * [First odd prime in the (n-th)-order Fibonacci sequence Fn](./oeis-research/Jacques%20Tramu/First%20odd%20prime%20in%20the%20(n-th)-order%20Fibonacci%20sequence%20Fn)
             * [prog.pl](./oeis-research/Jacques%20Tramu/First%20odd%20prime%20in%20the%20(n-th)-order%20Fibonacci%20sequence%20Fn/prog.pl)
@@ -1643,6 +1658,9 @@ Highly experimental personal projects.
         * [First k such that if x(1) = k and x(i+1) = A062028(x(i)), x(1) to x(n) are all semiprimes but x(n+1) is not](./oeis-research/Robert%20Israel/First%20k%20such%20that%20if%20x(1)%20=%20k%20and%20x(i+1)%20=%20A062028(x(i)),%20x(1)%20to%20x(n)%20are%20all%20semiprimes%20but%20x(n+1)%20is%20not)
             * [prog.pl](./oeis-research/Robert%20Israel/First%20k%20such%20that%20if%20x(1)%20=%20k%20and%20x(i+1)%20=%20A062028(x(i)),%20x(1)%20to%20x(n)%20are%20all%20semiprimes%20but%20x(n+1)%20is%20not/prog.pl)
             * [prog 2.pl](./oeis-research/Robert%20Israel/First%20k%20such%20that%20if%20x(1)%20=%20k%20and%20x(i+1)%20=%20A062028(x(i)),%20x(1)%20to%20x(n)%20are%20all%20semiprimes%20but%20x(n+1)%20is%20not/prog_2.pl)
+        * [First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n](./oeis-research/Robert%20Israel/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n)
+            * [prog.pl](./oeis-research/Robert%20Israel/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/prog.pl)
+            * [upperbounds.pl](./oeis-research/Robert%20Israel/First%20number%20k%20such%20that%20k%20+%20a(i)%20has%20n%20prime%20factors,%20counted%20with%20multiplicity,%20for%20all%20i%20<%20n/upperbounds.pl)
         * [First number that is the sum of k successive semiprimes for 1 <= k <= n](./oeis-research/Robert%20Israel/First%20number%20that%20is%20the%20sum%20of%20k%20successive%20semiprimes%20for%201%20<=%20k%20<=%20n)
             * [prog.pl](./oeis-research/Robert%20Israel/First%20number%20that%20is%20the%20sum%20of%20k%20successive%20semiprimes%20for%201%20<=%20k%20<=%20n/prog.pl)
             * [prog memory friendly.pl](./oeis-research/Robert%20Israel/First%20number%20that%20is%20the%20sum%20of%20k%20successive%20semiprimes%20for%201%20<=%20k%20<=%20n/prog_memory_friendly.pl)
diff --git a/oeis-research/Daniel Suteu/First number k such that k + a(i) has n distinct prime factors, for all i < n/prog.sf b/oeis-research/Daniel Suteu/First number k such that k + a(i) has n distinct prime factors, for all i < n/prog.sf
new file mode 100644
index 0000000..2bc1d96
--- /dev/null
+++ b/oeis-research/Daniel Suteu/First number k such that k + a(i) has n distinct prime factors, for all i < n/prog.sf	
@@ -0,0 +1,30 @@
+#!/usr/bin/ruby
+
+# a(n) is the first number k such that k + a(i) has n distinct prime factors, for all i < n; a(0) = 0.
+# https://oeis.org/A??????
+
+# Known terms:
+#   0, 2, 10, 130, 8930, 1133900, 401424520
+
+func a(n) is cached {
+
+    return 0 if (n == 0);
+    var terms = (^n -> map(a).flip)
+
+    var lo = 1
+    var hi = 2*lo
+
+    loop {
+        n.omega_primes_each(lo, hi, {|k|
+            if (terms.all { is_omega_prime(k + _, n) }) {
+                return k
+            }
+        })
+        lo = hi+1
+        hi = 2*lo
+    }
+}
+
+for n in (1..10) {
+    say [n, a(n)]
+}
diff --git a/oeis-research/Daniel Suteu/First number k such that k + a(i) is the product of n distinct prime factors, for all i < n/prog.pl b/oeis-research/Daniel Suteu/First number k such that k + a(i) is the product of n distinct prime factors, for all i < n/prog.pl
new file mode 100644
index 0000000..89b2a38
--- /dev/null
+++ b/oeis-research/Daniel Suteu/First number k such that k + a(i) is the product of n distinct prime factors, for all i < n/prog.pl	
@@ -0,0 +1,101 @@
+#!/usr/bin/perl
+
+# a(n) is the first number k such that k + a(i) is the product of n distinct prime factors, for all i < n; a(0) = 0.
+# https://oeis.org/A??????
+
+# Known terms:
+#   0, 2, 33, 1309, 55165, 13386021, 2239003921
+
+# Lower-bounds:
+#   a(7) > 1649267441663, if it exists.
+
+use 5.036;
+use ntheory qw(:all);
+
+my @terms = (0, 2, 33, 1309, 55165, 13386021, 2239003921);
+
+sub squarefree_almost_prime_numbers ($A, $B, $k, $callback) {
+
+    $A = vecmax($A, powint(2, $k));
+
+    my $n = $k;
+
+    sub ($m, $p, $k) {
+
+        if ($k == 1) {
+
+            my $v;
+
+            forprimes {
+
+                $v = $m * $_;
+
+                if (    is_almost_prime($n, $v + $terms[-1])
+                    and is_almost_prime($n, $v + $terms[-2])
+                    and is_almost_prime($n, $v + $terms[-3])
+                    and is_square_free($v + $terms[-1])
+                    and is_square_free($v + $terms[-2])
+                    and is_square_free($v + $terms[-3])
+                    and vecall { is_almost_prime($n, $v + $_) and is_square_free($v + $_) } @terms) {
+                    $callback->($v);
+                    $B = $v if ($v < $B);
+                    lastfor;
+                }
+
+            } vecmax($p, cdivint($A, $m)), divint($B, $m);
+
+            return;
+        }
+
+        my $s = rootint(divint($B, $m), $k);
+
+        foreach my $q (@{primes($p, $s)}) {
+            __SUB__->($m * $q, $q+1, $k - 1);
+        }
+      }
+      ->(1, 2, $k);
+}
+
+my $n  = 7;
+my $lo = 2;
+my $hi = 2 * $lo;
+
+say "\n:: Searching for a($n)\n";
+
+while (1) {
+
+    say "Sieving: [$lo, $hi]";
+
+    my @terms;
+    squarefree_almost_prime_numbers(
+        $lo, $hi, $n,
+        sub($k) {
+            say "Found upper-bound: a($n) <= $k";
+            push @terms, $k;
+        }
+    );
+
+    @terms = sort { $a <=> $b } @terms;
+
+    if (@terms) {
+        say "New term: a($n) = $terms[0]\n";
+        last;
+    }
+
+    $lo = $hi + 1;
+    $hi = 2 * $lo;
+}
+
+__END__
+
+Sieving: [805306367, 1610612734]
+Sieving: [1610612735, 3221225470]
+Found upper-bound: a(6) <= 2239003921
+New term: a(6) = 2239003921
+
+perl prog.pl  28.40s user 0.04s system 92% cpu 30.751 total
+
+Sieving: [824633720831, 1649267441662]
+Sieving: [1649267441663, 3298534883326]
+^C
+perl prog.pl  6250.60s user 14.21s system 84% cpu 2:03:41.07 total
diff --git a/oeis-research/Daniel Suteu/First number k such that k + a(i) is the product of n distinct prime factors, for all i < n/prog.sf b/oeis-research/Daniel Suteu/First number k such that k + a(i) is the product of n distinct prime factors, for all i < n/prog.sf
new file mode 100644
index 0000000..1b13105
--- /dev/null
+++ b/oeis-research/Daniel Suteu/First number k such that k + a(i) is the product of n distinct prime factors, for all i < n/prog.sf	
@@ -0,0 +1,30 @@
+#!/usr/bin/ruby
+
+# a(n) is the first number k such that k + a(i) is the product of n distinct prime factors, for all i < n; a(0) = 0.
+# https://oeis.org/A??????
+
+# Known terms:
+#   0, 2, 33, 1309, 55165, 13386021, 2239003921
+
+func a(n) is cached {
+
+    return 0 if (n == 0);
+    var terms = (^n -> map(a).flip)
+
+    var lo = 1
+    var hi = 2*lo
+
+    loop {
+        n.squarefree_almost_primes_each(lo, hi, {|k|
+            if (terms.all { is_squarefree_almost_prime(k + _, n) }) {
+                return k
+            }
+        })
+        lo = hi+1
+        hi = 2*lo
+    }
+}
+
+for n in (1..10) {
+    say "a(#{n}) = #{a(n)}"
+}
diff --git a/oeis-research/Daniel Suteu/First number k such that the concatenation of a(i) and k has n distinct prime factors, for all i < n/prog.sf b/oeis-research/Daniel Suteu/First number k such that the concatenation of a(i) and k has n distinct prime factors, for all i < n/prog.sf
new file mode 100644
index 0000000..e20c66e
--- /dev/null
+++ b/oeis-research/Daniel Suteu/First number k such that the concatenation of a(i) and k has n distinct prime factors, for all i < n/prog.sf	
@@ -0,0 +1,30 @@
+#!/usr/bin/ruby
+
+# a(n) is the irst number k such that the concatenation of a(i) and k has n distinct prime factors, for all i < n; a(0) = 0.
+# https://oeis.org/A??????
+
+# Known terms:
+#   0, 2, 6, 66, 210, 22110, 9958740
+
+func a(n) is cached {
+
+    return 0 if (n == 0);
+    var terms = (^n -> map(a).flip)
+
+    var lo = 1
+    var hi = 2*lo
+
+    loop {
+        n.omega_primes_each(lo, hi, {|k|
+            if (terms.all { is_omega_prime(Num(join('', _, k)), n) }) {
+                return k
+            }
+        })
+        lo = hi+1
+        hi = 2*lo
+    }
+}
+
+for n in (1..10) {
+    say "a(#{n}) = #{a(n)}"
+}
diff --git a/oeis-research/Daniel Suteu/First number k such that the concatenation of a(i) and k has n prime factors, counted with multiplicity, for all i < n/prog.sf b/oeis-research/Daniel Suteu/First number k such that the concatenation of a(i) and k has n prime factors, counted with multiplicity, for all i < n/prog.sf
new file mode 100644
index 0000000..2a26dbc
--- /dev/null
+++ b/oeis-research/Daniel Suteu/First number k such that the concatenation of a(i) and k has n prime factors, counted with multiplicity, for all i < n/prog.sf	
@@ -0,0 +1,30 @@
+#!/usr/bin/ruby
+
+# a(n) is the irst number k such that the concatenation of a(i) and k has n prime factors, counted with multiplicity, for all i < n; a(0) = 0.
+# https://oeis.org/A??????
+
+# Known terms:
+#   0, 2, 6, 8, 152, 920, 2256, 57824, 223520, 612500, 14103168, 110125568
+
+func a(n) is cached {
+
+    return 0 if (n == 0);
+    var terms = (^n -> map(a).flip)
+
+    var lo = 1
+    var hi = 2*lo
+
+    loop {
+        n.almost_primes_each(lo, hi, {|k|
+            if (terms.all { is_almost_prime(Num(join('', _, k)), n) }) {
+                return k
+            }
+        })
+        lo = hi+1
+        hi = 2*lo
+    }
+}
+
+for n in (1..100) {
+    say "a(#{n}) = #{a(n)}"
+}
diff --git a/oeis-research/Daniel Suteu/First number k such that the concatenation of k and a(i) has n distinct prime factors, for all i < n/prog.sf b/oeis-research/Daniel Suteu/First number k such that the concatenation of k and a(i) has n distinct prime factors, for all i < n/prog.sf
new file mode 100644
index 0000000..92fb309
--- /dev/null
+++ b/oeis-research/Daniel Suteu/First number k such that the concatenation of k and a(i) has n distinct prime factors, for all i < n/prog.sf	
@@ -0,0 +1,30 @@
+#!/usr/bin/ruby
+
+# a(n) is the irst number k such that the concatenation of k and a(i) has n distinct prime factors, for all i < n; a(0) = 1.
+# https://oeis.org/A??????
+
+# Known terms:
+#   1, 3, 14, 804, 48330, 16579170
+
+func a(n) is cached {
+
+    return 1 if (n == 0);
+    var terms = (^n -> map(a).flip)
+
+    var lo = 1
+    var hi = 2*lo
+
+    loop {
+        n.omega_primes_each(lo, hi, {|k|
+            if (terms.all { is_omega_prime(Num(join('', k, _)), n) }) {
+                return k
+            }
+        })
+        lo = hi+1
+        hi = 2*lo
+    }
+}
+
+for n in (1..10) {
+    say "a(#{n}) = #{a(n)}"
+}
diff --git a/oeis-research/Daniel Suteu/First number k such that the concatenation of k and a(i) has n prime factors, counted with multiplicity, for all i < n/prog.sf b/oeis-research/Daniel Suteu/First number k such that the concatenation of k and a(i) has n prime factors, counted with multiplicity, for all i < n/prog.sf
new file mode 100644
index 0000000..45138fe
--- /dev/null
+++ b/oeis-research/Daniel Suteu/First number k such that the concatenation of k and a(i) has n prime factors, counted with multiplicity, for all i < n/prog.sf	
@@ -0,0 +1,30 @@
+#!/usr/bin/ruby
+
+# a(n) is the irst number k such that the concatenation of k and a(i) has n prime factors, counted with multiplicity, for all i < n; a(0) = 1.
+# https://oeis.org/A??????
+
+# Known terms:
+#   1, 3, 9, 555, 18762, 1516626
+
+func a(n) is cached {
+
+    return 1 if (n == 0);
+    var terms = (^n -> map(a).flip)
+
+    var lo = 1
+    var hi = 2*lo
+
+    loop {
+        n.almost_primes_each(lo, hi, {|k|
+            if (terms.all { is_almost_prime(Num(join('', k, _)), n) }) {
+                return k
+            }
+        })
+        lo = hi+1
+        hi = 2*lo
+    }
+}
+
+for n in (1..100) {
+    say "a(#{n}) = #{a(n)}"
+}
diff --git a/oeis-research/J.W.L. (Jan) Eerland/Smallest k such that 3^(4*3^n) - k is a safe prime/prog.sf b/oeis-research/J.W.L. (Jan) Eerland/Smallest k such that 3^(4*3^n) - k is a safe prime/prog.sf
new file mode 100644
index 0000000..61fd659
--- /dev/null
+++ b/oeis-research/J.W.L. (Jan) Eerland/Smallest k such that 3^(4*3^n) - k is a safe prime/prog.sf	
@@ -0,0 +1,52 @@
+#!/usr/bin/ruby
+
+# Smallest k such that 3^(4*3^n) - k is a safe prime.
+# https://oeis.org/A376946
+
+# Known terms:
+#   22, 202, 6934, 634, 109678, 445294, 2323138
+
+# Lower-bounds:
+#   a(7) > 23348433
+
+func a(n, from=1) {
+
+    var prefix = 3**(4 * 3**n)
+    var len = prefix.len
+
+    for k in (from .. Inf) {
+        say "Testing: #{k} (length: #{len})"
+
+        local Num!USE_PFGW = false
+
+        if (primality_pretest(prefix - k) && primality_pretest((prefix - k - 1)>>1)) {
+
+             local Num!USE_PFGW = true
+
+            if (prefix - k -> is_safe_prime) {
+                return k
+            }
+        }
+    }
+}
+
+var n = 7
+var from = 23348433
+
+say "a(#{n}) = #{a(n, from)}"
+
+#for n in (0..100) {
+#    say [n, a(n)]
+#}
+
+__END__
+[0, 22]
+[2, 6934]
+[3, 634]
+[4, 109678]
+[5, 445294]
+[6, 2323138]
+
+Testing: 14194858 (length: 4174)
+^C
+/home/swampyx/Other/Programare/sidef/bin/sidef -N  prog.sf  20260.40s user 1064.73s system 95% cpu 6:13:50.82 total
diff --git a/oeis-research/Robert Israel/First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n/prog.pl b/oeis-research/Robert Israel/First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n/prog.pl
new file mode 100644
index 0000000..113d7a0
--- /dev/null
+++ b/oeis-research/Robert Israel/First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n/prog.pl	
@@ -0,0 +1,122 @@
+#!/usr/bin/perl
+
+# a(n) is the first number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n; a(0) = 0.
+# https://oeis.org/A361228
+
+# Known terms:
+#   0, 2, 4, 66, 1012, 14630, 929390, 63798350
+
+# New terms:
+#   a(8) = 19371451550
+
+# Lower-bounds:
+#   a(9) > 824633720831
+
+use 5.036;
+use ntheory qw(:all);
+
+my @terms = (0, 2, 4, 66, 1012, 14630, 929390, 63798350, 19371451550);
+
+sub almost_prime_numbers ($A, $B, $k, $callback) {
+
+    $A = vecmax($A, powint(2, $k));
+
+    my $n = $k;
+
+    sub ($m, $p, $k) {
+
+        if ($k == 1) {
+
+            my $v;
+
+            forprimes {
+
+                $v = $m * $_;
+
+                if (    is_almost_prime($n, $v + $terms[-1])
+                    and is_almost_prime($n, $v + $terms[-2])
+                    and is_almost_prime($n, $v + $terms[-3])
+                    and vecall { is_almost_prime($n, $v + $_) } @terms) {
+                    $callback->($v);
+                    $B = $v if ($v < $B);
+                    lastfor;
+                }
+
+            } vecmax($p, cdivint($A, $m)), divint($B, $m);
+
+            return;
+        }
+
+        my $s = rootint(divint($B, $m), $k);
+
+        foreach my $q (@{primes($p, $s)}) {
+            __SUB__->($m * $q, $q, $k - 1);
+        }
+      }
+      ->(1, 2, $k);
+}
+
+my $n  = 9;
+my $lo = 2;
+my $hi = 2 * $lo;
+
+say "\n:: Searching for a($n)\n";
+
+while (1) {
+
+    say "Sieving: [$lo, $hi]";
+
+    my @terms;
+    almost_prime_numbers(
+        $lo, $hi, $n,
+        sub($k) {
+            say "Found upper-bound: a($n) <= $k";
+            push @terms, $k;
+        }
+    );
+
+    @terms = sort { $a <=> $b } @terms;
+
+    if (@terms) {
+        say "New term: a($n) = $terms[0]\n";
+        last;
+    }
+
+    $lo = $hi + 1;
+    $hi = 2 * $lo;
+}
+
+__END__
+:: Searching for a(7)
+
+Sieving: [929391, 1858782]
+Sieving: [1858783, 3717566]
+Sieving: [3717567, 7435134]
+Sieving: [7435135, 14870270]
+Sieving: [14870271, 29740542]
+Sieving: [29740543, 59481086]
+Sieving: [59481087, 118962174]
+Found upper-bound: a(7) <= 63798350
+New term: a(7) = 63798350
+
+:: Searching for a(8)
+
+Sieving: [63798351, 127596702]
+Sieving: [127596703, 255193406]
+Sieving: [255193407, 510386814]
+Sieving: [510386815, 1020773630]
+Sieving: [1020773631, 2041547262]
+Sieving: [2041547263, 4083094526]
+Sieving: [4083094527, 8166189054]
+Sieving: [8166189055, 16332378110]
+Sieving: [16332378111, 32664756222]
+Found upper-bound: a(8) <= 19371451550
+New term: a(8) = 19371451550
+
+perl prog.pl  462.44s user 0.42s system 92% cpu 8:18.36 total
+
+Sieving: [206158430207, 412316860414]
+Sieving: [412316860415, 824633720830]
+Sieving: [824633720831, 1649267441662]
+^C
+perl prog.pl  13057.94s user 21.68s system 87% cpu 4:09:52.99 total
diff --git a/oeis-research/Robert Israel/First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n/upperbounds.pl b/oeis-research/Robert Israel/First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n/upperbounds.pl
new file mode 100644
index 0000000..a2bcfdb
--- /dev/null
+++ b/oeis-research/Robert Israel/First number k such that k + a(i) has n prime factors, counted with multiplicity, for all i < n/upperbounds.pl	
@@ -0,0 +1,23 @@
+#!/usr/bin/perl
+
+use 5.036;
+use ntheory qw(:all);
+
+my @terms = (0, 2, 4, 66, 1012, 14630, 929390, 63798350, 19371451550);
+
+my $prefix = 40150;
+
+my $n = 9;
+
+foralmostprimes {
+
+    my $t = $prefix * $_;
+
+    if (    is_almost_prime($n, $t + $terms[-1])
+        and is_almost_prime($n, $t + $terms[-2])
+        and is_almost_prime($n, $t + $terms[-3])
+        and vecall { is_almost_prime($n, $t + $_) } @terms) {
+        die "Found: a($n) <= $t";
+    }
+
+} $n - prime_bigomega($prefix), 1e9;
diff --git a/oeis-research/Zak Seidov/First number k such that Omega(k) = n and Omega(n - 1) = Omega(n + 1) = n + 1/generate.pl b/oeis-research/Zak Seidov/First number k such that Omega(k) = n and Omega(n - 1) = Omega(n + 1) = n + 1/generate.pl
index cade179..e6e4ed1 100644
--- a/oeis-research/Zak Seidov/First number k such that Omega(k) = n and Omega(n - 1) = Omega(n + 1) = n + 1/generate.pl	
+++ b/oeis-research/Zak Seidov/First number k such that Omega(k) = n and Omega(n - 1) = Omega(n + 1) = n + 1/generate.pl	
@@ -7,7 +7,7 @@
 #   5, 51, 343, 3185, 75951, 1780624, 16825375, 212781249
 
 # New terms:
-#   a(9) = 4613781249
+#   a(9)  = 4613781249
 #   a(10) = 74239460225
 #   a(11) = 858245781249