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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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2
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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
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OFFSET
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1,1
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COMMENTS
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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, Nov 11 2005
No other n<50000. All n<=1406 yield provable primes. - T. D. Noe, Mar 08 2006
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LINKS
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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)).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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