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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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6
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1, 5, 49, 1261, 62689, 7629469, 1294716361, 375074829229, 135662633811769, 71859617272521901, 60483708554835755641, 58166700851687469003901, 79670437976161330893757369, 133981073592392620630139873389
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 94-98.
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LINKS
| S. R. Finch, Meissel-Mertens Constants
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FORMULA
| 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
| a(2) = 49 so a(3) = 49*p(3)^2 + (2*3)^2 = 49*25 + 36 = 1261.
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MATHEMATICA
| 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
| Cf. A061015, A075987, A024528.
Sequence in context: A001819 A064618 A193199 * A084765 A203411 A082795
Adjacent sequences: A075983 A075984 A075985 * A075987 A075988 A075989
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KEYWORD
| nonn,frac
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Sep 28 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 30 2002
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