A358621 Smallest b > 1 such that b^(2^n)+1 is a Sophie Germain prime.

2, 2, 160, 140, 2800, 8660, 62150, 4085530, 922820, 4629490, 5802710, 1146175000, 90894850

Offset

0,1

Comments

In other words, 2*b^(2^n)+3 is also prime.

For n > 1, a(n) ends in 0 because b is even (or else b^(2^n)+1 would have 2 as a proper divisor) and b == 0 (mod 5) (or else 2*b^(2^n)+3 would have 5 as a proper divisor).

Links

Table of n, a(n) for n=0..12.

PrimeGrid and "Stream", GFN-1x Small Primes search, mentions a(12).

Prog

(PARI) a(n)=n<2&&return(2); forstep(b=10, +oo, 10, ispseudoprime(b^(2^n)+1)&&ispseudoprime(2*b^(2^n)+3)&&return(b))

Crossrefs

Cf. A005384, A056993, A182154.

Sequence in context: A376440 A003110 A100956 * A304915 A216481 A078241

Adjacent sequences: A358618 A358619 A358620 * A358622 A358623 A358624

Keyword

nonn,hard,more

Author

Jeppe Stig Nielsen, Nov 23 2022

Status

approved