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A185343
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Least number k such that k*p+1 divides 2^p+1 where p is prime(n), or 0 if no such number exists.
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0
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2, 0, 2, 6, 62, 210, 2570, 9198, 121574, 2, 23091222, 48, 2, 68186767614, 6, 2, 48, 12600235023025650, 109368, 794502, 24, 2550476412689091085878, 6, 2, 10, 8367330694575771627040945250, 4030501264, 6, 955272, 2, 446564785985483547852197647548252246, 8, 8, 32424, 8
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OFFSET
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1,1
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COMMENTS
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Akin to A186283 except for 2^p+1 and restricted to primes.
The larger terms of this sequence occur for the primes p > 3 in sequence A000978. These large terms are (2^p-2)/(3p).
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LINKS
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Table of n, a(n) for n=1..35.
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EXAMPLE
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2^3+1 = 9 has no factor of the form k*3+1, so a(primepi(3)) = a(2) = 0.
2^29+1 = 536870913 has factor 2*29+1=59, so a(primepi(29)) = a(10) = 2.
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MATHEMATICA
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Table[q = First /@ FactorInteger[2^p + 1]; s = Select[q, Mod[#1, p] == 1 &, 1]; If[s == {}, 0, (s[[1]] - 1)/p], {p, Prime[Range[30]]}]
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CROSSREFS
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Cf. A098268 , A186283.
Sequence in context: A242840 A081081 A111111 * A161014 A235712 A154852
Adjacent sequences: A185340 A185341 A185342 * A185344 A185345 A185346
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KEYWORD
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easy,nonn
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AUTHOR
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Bill McEachen, Feb 26 2011
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STATUS
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approved
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