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Search: id:A123627
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| A123627 |
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Smallest prime q such that (q^p+1)/(q+1) is prime, where p = Prime[n]; or 0 if no such prime q exists. |
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+0
2
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| 0, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 19, 61, 2, 7, 839, 89, 2, 5, 409, 571, 2, 809, 227, 317, 2, 5, 79, 23, 4073, 2, 281, 89, 739, 1427, 727, 19, 19, 2, 281, 11, 2143, 2, 1013, 4259, 2, 661, 1879, 401, 5, 4099, 1579, 137, 43, 487, 307, 547, 1709, 43, 3, 463
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(1) = 0 because such a prime does not exist, Mod[n^2+1,n+1] = 2 for n>1. Corresponding primes (q^p+1)/(q+1), where prime q = a(n) and p = Prime[n], are listed in A123628[n] = {1,3,11,43,683,2731,43691,174763,2796203,402488219476647465854701,715827883,...}. A123628(n) = (a(n)^Prime[n] + 1) / (a(n) + 1). a(n) coincides with A103795[n] when A103795[n] is prime. a(n) = 2 for n = PrimePi[A000978[k]] = {2,3,4,5,6,7,8,9,11,14,18,22,26,31,39,43,46,65,69,126,267,380,495,762,1285,1304,1364,1479,1697,4469,8135,9193,11065,11902,12923,13103,23396,23642,31850,...}. Corresponding primes of the form (2^p + 1)/3 are the Wagstaff primes that are listed in A000979[n] = {3,11,43,683,2731,43691,174763,2796203,715827883,...}.
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MATHEMATICA
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a(1) = 0, for n>1 Do[p=Prime[k]; n=1; q=Prime[n]; cp=(q^p+1)/(q+1); While[ !PrimeQ[cp], n=n+1; q=Prime[n]; cp=(q^p+1)/(q+1)]; Print[q], {k, 2, 61}]
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CROSSREFS
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Cf. A123628, A103795, A123487, A123488, A000978, A000979.
Sequence in context: A008857 A047935 A103795 this_sequence A001991 A052298 A081412
Adjacent sequences: A123624 A123625 A123626 this_sequence A123628 A123629 A123630
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KEYWORD
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hard,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 04 2006
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