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Search: id:A111354
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| A111354 |
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Numbers n such that the numerator of sum_{i=1..n}(1/i^2), in reduced form, is prime. |
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+0
3
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| 2, 7, 13, 19, 121, 188, 252, 368, 605, 745, 1085, 1127, 1406, 1743, 1774, 2042, 2087, 2936, 3196, 3207, 3457, 4045, 7584, 10307, 12603, 12632, 14438, 14526, 14641, 15662, 15950, 16261, 18084, 18937, 19676, 40984, 45531, 46009, 48292, 48590
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Numbers n such that A007406[n] is prime.
Some of the larger entries may only correspond to probable primes.
A007406[n] are the Wolstenholme numbers: numerator of Sum 1/k^2, k = 1..n. Primes in A007406[n] are listed in A123751[n] = A007406[a(n)] = {5,266681,40799043101,86364397717734821,...}.
For prime p>3, Wolstenholme's theorem says that p divides A007406(p-1). Hence n+1 cannot be prime for any n>2 in this sequence. - 12 more terms from T. D. Noe (noe(AT)sspectra.com), Nov 11 2005
No other n<50000. All n<=1406 yield provable primes. - T. D. Noe (noe(AT)sspectra.com), Mar 08 2006
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LINKS
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Eric Weisstein's World of Mathematics, Wolstenholme's Theorem
Eric Weisstein's World of Mathematics, Harmonic Number.
Eric Weisstein's World of Mathematics, Wolstenholme Number
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EXAMPLE
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A007406[n] begins {1, 5, 49, 205, 5269, 5369, 266681, 1077749, 9778141,...}.
Thus a(1) = 2 because A007406[2] = 5 is prime but A007406[1] = 1 is not prime.
a(2) = 7 because A007406[7] = 266681 is prime but all A007406[k] are composite for 2 < k < 7.
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MATHEMATICA
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s = 0; Do[s += 1/n^2; If[PrimeQ[Numerator[s]], Print[n]], {n, 1, 10^4}]
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CROSSREFS
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Cf. A007406 (numerator of sum_{i=1..n}(1/i^2)).
Cf. A123751, A001008, A007407, A067567, A056903.
Sequence in context: A053977 A079381 A079382 this_sequence A106675 A022946 A010895
Adjacent sequences: A111351 A111352 A111353 this_sequence A111355 A111356 A111357
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KEYWORD
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nonn
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AUTHOR
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Ryan Propper (rpropper(AT)stanford.edu), Nov 05 2005
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EXTENSIONS
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12 more terms from T. D. Noe (noe(AT)sspectra.com), Nov 11 2005
More terms from T. D. Noe (noe(AT)sspectra.com), Mar 08 2006
Additional comments from Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 11 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 11 2006
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