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Search: id:A165235
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| A165235 |
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Least prime p such that the n+1 numbers p + 2^k - 2, k=1..n+1, are all prime. |
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1
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| 3, 5, 5, 17, 17, 1607, 1607, 19427, 2397347207, 153535525937
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Eric W. Weisstein, MathWorld: Prime k-Tuples Conjecture
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EXAMPLE
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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.
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MATHEMATICA
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p=3; Table[While[ !And@@PrimeQ[p+2^Range[2, n+1]-2], p=NextPrime[p]]; p, {n, 8}]
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CROSSREFS
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Cf. A000918 (2^n - 2)
Sequence in context: A137780 A079372 A055382 this_sequence A072624 A147976 A019247
Adjacent sequences: A165232 A165233 A165234 this_sequence A165236 A165237 A165238
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 09 2009
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