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A125503
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Smallest number k such that the numerator of generalized harmonic number H(k,n) = Sum[ 1/i^n, {i,1,k} ] is a prime.
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1
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2, 2, 3, 2, 23, 73, 15, 2, 3, 5, 13, 57, 3, 171, 5, 2, 21, 7, 55, 152, 26, 1298, 115, 139, 3, 2019, 3, 4, 3, 15, 56, 177
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OFFSET
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1,1
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COMMENTS
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a(n) = 2 for n = {1,2,4,8,16,...}. Corresponding Fermat primes A019434 = {3, 5, 17, 257, 65537, ...}. a(n) = 3 for n = {3,9,13,25,27,29,95,107,153,159,...}. a(n) = 5 for n = {10,15,60,90,197,209,...}. a(n) = 7 for n = {18,47,112,155,273,...}. a(n) = 15 for n = {7,30,43,...}. a(28) = 4. a(31) = 56. a(144) = 9.
Contribution from Alexander Adamchuk, Apr 18 2010: (Start)
a(27)-a(32) = {3,4,3,15,56,177}.
a(n) = 3 for all n>2 listed in A125706. (End)
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LINKS
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Table of n, a(n) for n=1..32.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Harmonic Number.
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MATHEMATICA
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Do[n = 1; f = 0; While[Not[PrimeQ[Numerator[f]]], f = f + 1/n^x; n++ ]; Print[{x, n - 1}], {x, 1, 25}] [From Alexander Adamchuk, Apr 18 2010]
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CROSSREFS
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Cf. A001008, A007406, A007408, A007410, A099828.
Cf. A019434.
A125706. [From Alexander Adamchuk, Apr 18 2010]
Sequence in context: A110088 A064998 A127012 * A127009 A181313 A164089
Adjacent sequences: A125500 A125501 A125502 * A125504 A125505 A125506
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KEYWORD
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hard,more,nonn
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AUTHOR
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Alexander Adamchuk, Dec 28 2006, Jan 31 2007
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EXTENSIONS
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a(22)-a(25) from Alexander Adamchuk, Apr 18 2010
a(26)-a(32) from Alexander Adamchuk, Apr 26 2010
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STATUS
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approved
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