experimental-projects/oeis-research/Daniel Suteu/Smallest Fermat base-2 pseudoprime such that gpf(p-1) = prime(n)/prog.sf

#!/usr/bin/ruby

# a(n) is the smallest Fermat pseudoprime to base 2 such that gpf(p-1) = prime(n) for all prime factors p of a(n).

# a(1)  = 4369
# a(2)  = 1387
# a(3)  = 341
# a(4)  = 3277
# a(5)  = 2047
# a(6)  = 8321
# a(7)  = 31621
# a(8)  = 104653
# a(9)  = 280601
# a(10) = 13747
# a(11) = 2081713
# a(12) = 88357
# a(13) = 8902741
# a(14) = 741751
# a(15) = 665333
# a(16) = 680627
# a(17) = 2008597
# a(18) = 1252697
# a(19) = 3235699
# a(20) = 1293337

# Lower bound:
#   a(n) >= (2*p + 1)*(2*3*p + 1), where p = prime(n).

func a(n) {
    var p = prime(n)
    var from = (2*p + 1)*(2*3*p + 1)
    from..Inf -> first {|k|
        k.is_composite && k.is_pseudoprime(2) && k.factor.all { .dec.gpf == p }
    }
}

for n in (1..10) {
    say ("a(#{n}) = ", a(n))
}