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Search: id:A075987
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| A075987 |
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Numerator[1+1/p(1)^3+ ... + 1/p(n)^3] where p(k) = k-th prime. |
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5
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| 1, 9, 251, 31591, 10862713, 14467532003, 31797494201591, 156248170093443583, 1071839248022015186797, 13041980716182955257968099, 318091971114753602661286869511, 9476548712979446302049526230869201
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The sum in the sequence has limit 1.1747626393. The case of reciprocal squares is in A075986.
For n>0 a(n) is the determinant of the n X n matrix with elements M[i,j] = 1+Prime[i]^3 if i=j and 1 otherwise. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 08 2006
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LINKS
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Simon Plouffe, Plouffe's Inverter
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FORMULA
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a(0)=1; a(n)=a(n-1)*p(n)^3+(p(1)*...*p(n-1))^3.
a(n) = Det[DiagonalMatrix[Table[Prime[i]^3,{i,1,n}]]+1] for n>0. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 08 2006
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EXAMPLE
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a(2) = 251 so a(3) = 251*p(3)^3 + (2*3)^3 = 251*125 + 216 = 31591.
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MATHEMATICA
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Table[Det[DiagonalMatrix[Table[Prime[i]^3, {i, 1, n}]]+1], {n, 1, 15}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 08 2006
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CROSSREFS
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Cf. A061015, A075986.
Sequence in context: A007408 A066989 A160501 this_sequence A135099 A073427 A158621
Adjacent sequences: A075984 A075985 A075986 this_sequence A075988 A075989 A075990
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Sep 28 2002
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