verify.sf

#!/usr/bin/ruby

# a(n) is the least k such that k^2 + 1 is a semiprime p*q, p < q, and (q - p)/2^n is prime.
# https://oeis.org/A258780

# The corresponding primes are:
#   2, 3, 71, 7, 1069, 7, 5, 5, 59, 2, 368471, 180463, 12421, 2, 29, 125683, 226169, 5, 369704891, 197, 5, 263, 7444559, 239621423, 594271, 2, 474359, ...

[

8, 12, 140, 64, 2236, 196, 1300, 1600, 6256, 5084, 248756, 246196, 484400, 36680, 887884, 821836, 1559116, 104120, 126072244, 9586736, 4156840, 542759984, 1017981724, 2744780140, 405793096, 148647496, 1671024916

#~ 542759984
#~ 1017981724
#~ 2744780140
#~ 405793096
#~ 148647496
#~ 1671024916

].each_kv{|k,v|

    var n = (k+2)
    assert(v**2 + 1 -> is_semiprime)
    var (a,b) = factor(v**2 + 1)...
    assert((b-a) / 2**n -> is_int)
    assert((b-a) / 2**n -> is_prime)

    say [v, (b-a) / 2**n, n]
    #print(b-a / 2**n, ", ")
}