prog.sf

#!/usr/bin/ruby

# a(n) is the least number of the form p^2 + q^2 - 2 for primes p and q that is an odd prime times 2^n, or -1 if there is no such number
# https://oeis.org/A359492

# Known terms:
#   11, 6, -1, 56, 48, 96, 192, 384, 2816, 1536, 109568, 10582016, 12288, 7429922816, 64176128, 4318724096, 196608, 60486975488, 9388028592128

# New terms found:
#   a(19) = 849566088298496

func a(n) {
    var t = 2**n

    each_prime(3, 1e13, {|p|
    #each_prime(381469721, 1e13, {|p|

        if (sum_of_squares(t*p + 2).any{.all_prime}) {
            return (t*p)
        }
    })

    return -1
}

for n in (3..100) {
    say "a(#{n}) = #{a(n)}"
}

__END__
a(3) = 56
a(4) = 48
a(5) = 96
a(6) = 192
a(7) = 384
a(8) = 2816
a(9) = 1536
a(10) = 109568
a(11) = 10582016
a(12) = 12288
a(13) = 7429922816
a(14) = 64176128
a(15) = 4318724096
a(16) = 196608
a(17) = 60486975488
a(18) = 9388028592128
a(19) = 849566088298496
a(20) = 214058289594368
a(21) = 896029329195008

__END__
a(19) = 849566088298496
sidef prog.sf  6557.60s user 18.65s system 92% cpu 1:58:41.70 total