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Search: id:A075986
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| A075986 |
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Numerator of 1+1/p(1)^2+ ... + 1/p(n)^2 where p(k) = k-th prime. |
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+0
7
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| 1, 5, 49, 1261, 62689, 7629469, 1294716361, 375074829229, 135662633811769, 71859617272521901, 60483708554835755641, 58166700851687469003901, 79670437976161330893757369, 133981073592392620630139873389
(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 is similar to that in A061015 with an additional 1. The sum in the definition has limit about 1.45224742. The case of reciprocal cubes is in A075987.
For n>0 a(n) is the determinant of the n X n matrix with elements M[i,j] = 1+Prime[i]^2 if i=j and 1 otherwise. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 08 2006
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 94-98.
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LINKS
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S. R. Finch, Meissel-Mertens Constants
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FORMULA
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a(0)=1; a(n)=a(n-1)*p(n)^2+(p(1)*...*p(n-1))^2.
a(n) = Det[DiagonalMatrix[Table[Prime[i]^2,{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) = 49 so a(3) = 49*p(3)^2 + (2*3)^2 = 49*25 + 36 = 1261.
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MATHEMATICA
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Table[Det[DiagonalMatrix[Table[Prime[i]^2, {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, A075987.
Cf. A024528.
Sequence in context: A002111 A001819 A064618 this_sequence A084765 A082795 A059008
Adjacent sequences: A075983 A075984 A075985 this_sequence A075987 A075988 A075989
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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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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Sep 30 2002
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