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A165235 Least prime p such that the n+1 numbers p + 2^k - 2, k=1..n+1, are all prime. 0
3, 5, 5, 17, 17, 1607, 1607, 19427, 2397347207, 153535525937 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, Sep 09 2009
STATUS
approved

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Last modified May 25 01:41 EDT 2024. Contains 372782 sequences. (Running on oeis4.)