A050526 Primes of form 5*2^n+1.

11, 41, 641, 40961, 163841, 167772161, 2748779069441, 180143985094819841, 188894659314785808547841, 193428131138340667952988161, 850705917302346158658436518579420528641

Offset: 1

Author

N. J. A. Sloane, Dec 29 1999

Keywords

• nonn

Comments

All terms are odd since if n is even, then 5*2^n+1 is divisible by 3. - Michele Fabbrini, Jun 06 2021

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..12
• Ray Ballinger, Wilfried Keller, List of primes k*2^n + 1 for k < 300
• Wikipedia, Proth's theorem
• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Crossrefs

For the corresponding exponents n see A002254.

Cf. A019434, A039687, A050527, A050528, A050529, A195745, A300406, A300407, A300408.

Programs

GAP

Filtered(List([1..270], n->5*2^n + 1), IsPrime); # Muniru A Asiru, Mar 06 2018

Magma

[a: n in [1..200] | IsPrime(a) where a is 5*2^n + 1]; // Vincenzo Librandi, Mar 06 2018

Maple

a:=(n, k)->`if`(isprime(k*2^n+1), k*2^n+1, NULL):
seq(a(n, 5), n=1..127); # Martin Renner, Mar 05 2018

PARI

lista(nn) = {for(k=1, nn, if(ispseudoprime(p=5*2^k+1), print1(p, ", "))); } \\ Altug Alkan, Mar 29 2018

Formula

a(n) = A083575(A002254(n)). - Michel Marcus, Mar 29 2018