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Search: id:A138852
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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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+0
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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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T. Piezas, "More on e^(pi*sqrt(163))" on sci.math.research, Apr 13, 2008 and his Ramanujan Pages
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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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PROGRAM
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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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Cf. A139388, A138851, A003173, A014708, A056581 and references therein.
Sequence in context: A070655 A006263 A079236 this_sequence A062701 A020821 A020773
Adjacent sequences: A138849 A138850 A138851 this_sequence A138853 A138854 A138855
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Apr 17 2008
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