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Search: id:A115596
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| A115596 |
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The least number a(n)=k>1 such that (p+1)^k - p^k is prime, p = n-th prime. |
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1
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| 2, 2, 2, 7, 2, 3, 3, 5, 2, 2, 5, 3, 2, 37, 2, 17, 3, 61, 23, 7, 2, 2, 7, 5, 7, 59, 5, 2, 59, 2, 59, 3, 47, 2, 2, 43, 2, 3, 5, 31, 19, 7, 3, 5, 2, 2, 2, 37, 13, 17, 3, 2, 3, 2, 3, 7, 5, 79, 3, 7, 3, 2, 5, 5, 7, 7, 53, 2, 67, 2, 7, 79, 2, 5, 3, 5, 29, 17, 3, 37, 2, 3, 2, 3, 43, 3, 3, 3, 13, 3, 2, 5, 3, 5
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Values k=1 is omitted as in this case p is Sophie Germain prime (2p+1 is also prime) A005384.
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FORMULA
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p=n-th prime, (p+1)^k - p^k is prime, k>1 is minimal.
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EXAMPLE
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a(1)=2 because (2+1)^2-2^2=5 is prime;
a(14)=37 because p(14)=43 and
(43+1)^37-43^37=3679488080703419029992001830200360494989758810080014618823621
is prime.
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MATHEMATICA
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s={}; Do[n=Prime[i]; Do[If[PrimeQ[(n+1)^k-n^k], AppendTo[s, k]; Goto[ne]], {k, 2, 100}]; Label[ne], {i, 300}]; s
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CROSSREFS
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Cf. A005384.
Sequence in context: A129365 A021453 A053789 this_sequence A029610 A094246 A023573
Adjacent sequences: A115593 A115594 A115595 this_sequence A115597 A115598 A115599
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Jan 25 2006
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