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A138852
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Round(1/(x-round(x))), where x=(log(744+(12(p^2-1))^3)/Pi)^2, round(x) = nearest integer to x.
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2
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2, -4, 1435303, -2, 4, 4, -6, 17, 952364958135, -3, 4, -2, -5, -8, -7, -4, -2, 4, -10, 2, 21119108989115042, 2, -8, 4, -2, -7, 10, 3, 2, -3, -4, -6, -10, -16, -19, -16, -11, -7, -5, -3, -2, 2, 3, 6, -51, -5, -2, 3, 7, -10, -3, 3, 9, -6, -2, 5, -9, -2, 4, -8, -2, 6, -5, 2, 44, -3, 4, -5, 3, -35, -2, 10, -3, 5, -4
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OFFSET
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1,1
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COMMENTS
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Related to almost-integer values of e^(pi sqrt n), obtained for larger Heegener numbers (A003173): T. Piezas draws attention on the fact that the well-known integers very close to exp(pi sqrt(n)) are of the form (12(k^2-1))^3+744. Here this is expressed as the (rounded value) of the reciprocal of the (signed) distance from the integers of the n-value corresponding to a given integer k-value. As expected, records are obtained for k=3,9,21,231.
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LINKS
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EXAMPLE
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We have a(3) = 1435303 since (12(3^2-1))^3+744 = e^(pi sqrt(x)) with x = 19.0000006967... = 19+1/1435302.8.3...
In the same way, a(231)=43072298941682041177938098750 since (12(231^2-1))^3+744 = e^(pi sqrt(x)) with x = 163.0000000000000000000000000000232 = 163+1/43072298941682041177938098749.8977...
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PROG
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(PARI) default(realprecision, 200); A138852(n)={ n=(log(744+(12*(n^2-1))^3)/Pi)^2; round(1/(x-round(x))) }
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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