A029544 Near Cullen numbers: k such that (k+1)*2^k + 1 is prime.

0, 1, 2, 5, 6, 13, 26, 65, 66, 86, 114, 133, 186, 294, 445, 866, 1325, 1478, 1823, 2765, 7553, 7943, 10178, 20960, 20964, 21337, 26562, 85374, 96749, 247038

Offset: 1

Author

Henri Lifchitz

Keywords

• nonn
• more

Comments

Primes in the sequence are 2, 5, 13, 1823, 96749, ... - R. J. Mathar, Oct 15 2011

We can write (k+1)*2^k + 1 = {(k+1)/2}*4^{(k+1)/2} + 1, and when k is odd, this takes the form of a generalized Cullen prime (base 4). These are listed in A007646. In other words, {2*A007646 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019

Links

• Steven Harvey, NearCullen and NearWoodall Primes

Crossrefs

Cf. A002064, A007646, A230769.

Programs

PARI

isok(n) = isprime((n+1)*2^n+1); \\ Michel Marcus, Nov 09 2013

Extensions

Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008