A165235 Least prime p such that the n+1 numbers p + 2^k - 2, k=1..n+1, are all prime.

3, 5, 5, 17, 17, 1607, 1607, 19427, 2397347207, 153535525937

Offset

1,1

Comments

The n+1 primes have common differences of 2^k for k=1..n. For any n, the set {2^k - 2, k=1..n+1} is admissible. Hence by the prime k-tuple conjecture, an infinite number of primes p should exist for each n. Note that a(1) is the first term of the twin primes A001359 and a(2) is the first term of prime triples A022004. The a(12) term is greater than 10^12.

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, k-Tuple Conjecture

Example

a(5)=17 because {17,19,23,31,47,79} are 6 primes whose differences are powers of 2, and 17 is the least such prime.

Mathematica

p=3; Table[While[ !And@@PrimeQ[p+2^Range[2, n+1]-2], p=NextPrime[p]]; p, {n, 8}]

Crossrefs

Cf. A000918 (2^n - 2)

Sequence in context: A137780 A079372 A055382 * A370553 A200771 A072624

Adjacent sequences: A165232 A165233 A165234 * A165236 A165237 A165238

Keyword

hard,nonn

Author

T. D. Noe, Sep 09 2009

Status

approved