prog.sf

#!/usr/bin/ruby

# a(n) is the least k for which A237196(k) = n.
# https://oeis.org/A372648

# Known terms:
#   4, 10, 43, 1, 2, 26, 3, 28, 13, 2311675, 8396, 12918370, 37697697

var P = [nil]+1e5.primes

func a(n, pn=prime(n)) {

    return nil if (n <= 0)

    var t = 1

    for j in (1..Inf) {
        if (j != n) {
            t *= P[j]
        }
        if (is_composite(t+pn)) {
            if (j >= n) {
                return j-1
            }
            else {
                return j
            }
        }
    }

    return nil
}

assert_eq(a(2311675), 10)
assert_eq(a(8396), 11)
assert_eq(a(12918370), 12)
assert_eq(a(37697697), 13)

var table = []
var k = 1

1e9.each_prime {|p|
    var v = a(k, p)
    if (!table[v]) {
        table[v] = k
        say "a(#{v}) = #{k}"
    }
    ++k
}

__END__
a(4) = 1
a(5) = 2
a(7) = 3
a(1) = 4
a(2) = 10
a(9) = 13
a(6) = 26
a(8) = 28
a(3) = 43
a(11) = 8396