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A115596
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The least number 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, 58543, 2, 4663, 17, 3, 61, 23, 7, 2, 2, 7, 5, 7, 59, 5, 2, 59, 2, 196873
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OFFSET
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1,1
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COMMENTS
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Values k=1 is omitted as in this case p is Sophie Germain prime (2p+1 is also prime) A005384.
Each term is necessarily prime. Sophie Germain primes correspond to case k = 2. - Giuseppe Coppoletta, Oct 10 2018
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LINKS
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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]; k=2; While[!PrimeQ[(n+1)^k-n^k], k++]; AppendTo[s, k], {i, 14}]; s (* Amiram Eldar, Oct 12 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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