A230769 Numbers k such that (k+1)*2^k - 1 is prime.

1, 2, 3, 4, 5, 9, 14, 15, 16, 27, 45, 122, 125, 213, 242, 256, 263, 290, 855, 1059, 2273, 3945, 3999, 9512, 14127, 16486, 20056, 28834, 41493, 159147, 227139, 587823

Offset: 1

Author

Zak Seidov, Feb 23 2014

Keywords

• nonn
• more
• hard

Comments

1, 2 and 5 are the only terms of this sequence which are also in A029544. - Gerasimov Sergey, Feb 23 2014

The next term with this property is > 10000. - Michael B. Porter, Feb 23 2014

The probability of a given number N being a twin prime grows like 1/(log(N))^2, so for a given n, the probability that it has this property is 1/n^2, and the sum converges. Are there any n for which n*2^n-1 and n*2^n+1 are both prime? - Michael B. Porter, Feb 25 2014

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 Woodall prime (base 4). These are listed in A086661. In other words, {2*A086661 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019

The largest odd term currently known is 3986381 = 2*A086661(21) - 1. - Jeppe Stig Nielsen, Oct 16 2019

Links

• Steven Harvey, NearCullen and NearWoodall Primes
• Prime-Wiki, Near Generalized Woodall primes of the form (n+1)*2^n - 1

Crossrefs

Cf. A029544, A086661, A196273, A236752.

Programs

PARI

is_A230769(n) = ispseudoprime((n+1)*2^n-1) \\ M. F. Hasler, Mar 01 2014

Extensions

Edited and extended to values > 2273 by M. F. Hasler, Mar 01 2014

More terms from Jeppe Stig Nielsen, Oct 16 2019