A092262 Primes p which equal prime(2^k) - prime(2^(k-1)) + 1 for some k.

2, 5, 13, 79, 181, 409, 2053, 21011, 96487, 1235199066139957, 180572921869744273, 747909478827063599

Offset

1,1

Links

Table of n, a(n) for n=1..12.

Example

Prime(2^12)-prime(2^11) + 1 = 21011 is prime.

Mathematica

Select[#[[2]]-#[[1]]+1&/@Partition[Prime[2^Range[0, 30]], 2, 1], PrimeQ] (* Harvey P. Dale, Jul 08 2021 *)

Prog

(PARI) f(n)= for(x=1, n, y=prime(2^x)-prime(2^(x-1))+1; if(isprime(y), print1(y", ")))

Crossrefs

Cf. A345982 (values of k), A033844.

Sequence in context: A215167 A349735 A081650 * A365326 A096280 A236395

Adjacent sequences: A092259 A092260 A092261 * A092263 A092264 A092265

Keyword

nonn,more,hard

Author

Cino Hilliard, Feb 20 2004

Extensions

Corrected and edited by N. J. A. Sloane, following a suggestion from Harvey P. Dale, Jul 07 2021

a(10)-a(12) from Mohammed Yaseen, Jul 08 2021

Status

approved