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Search: id:A121240
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| A121240 |
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Numerator of Sum[ 1/2^p(k) {k,1,n} ], where p(k) = Prime[k]. |
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+0
1
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| 1, 3, 13, 53, 849, 3397, 54353, 217413, 3478609, 222630977, 890523909, 56993530177, 911896482833, 3647585931333, 58361374901329, 3735127993685057, 239048191595843649, 956192766383374597, 61196337048535974209
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Denominator of Sum[ 1/2^Prime[k], {k,1,n} ] equals 2^Prime[n] = A034765[n]. a(n) is prime for n = {2,3,4,10,21,321,...}. Prime a(n) are {3,13,53,222630977,...}. Prime Constant C = Sum[ 1/2^Prime[k], {k,1,Infinity}]. C = limit[ a(n)/2^Prime[n], n->Infinity ] = 0.41468250985111166... Decimal representation of Prime Constant is given in A051006[n].
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Prime Constant.
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FORMULA
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a(n) = Numerator[ Sum[ 1/2^Prime[k], {k,1,n} ] ]. a(n) = A072762[ Prime[n] ].
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MATHEMATICA
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Table[Numerator[Sum[1/2^Prime[k], {k, 1, n}]], {n, 1, 30}]
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CROSSREFS
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Cf. A034765, A072762, A051006, A010051.
Sequence in context: A072197 A065838 A052990 this_sequence A065839 A066611 A048514
Adjacent sequences: A121237 A121238 A121239 this_sequence A121241 A121242 A121243
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
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