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 A138851 Nearest integer to 1/(round(x)-x), where exp(Pi sqrt(n))-744 = (12(x^2-1))^3. 4
 -4, -3, -2, 2, 3, 5, 12, -33, -7, -4, -2, 2, 3, 6, 8954018, -6, -3, 2, 3, 9, -12, -3, -2, 4, 18, -6, -2, 3, 14, -5, -2, 4, -21, -3, 3, 51, -3, 3, 2683620901418, -3, 4, -9, 2, 11, -3, 4, -5, 3, -10, 2, -17, 2, -14, 2, -7, 3, -4, 7, -2, -16, 3, -3, 31514540715033062, 3, -3, -12, 5, 2, -3, -9, 12, 4, 2, -2, -3, -4, -7, -10, -16, -19, -16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 COMMENTS Records are attained at the larger Heegener numbers (A003173). T. Piezas draws attention on the fact that the integers very close to exp(pi sqrt(n)) are of the form (12(k^2-1))^3+744. Here this closeness is expressed as the (rounded value) of the reciprocal of the (signed) distance of these k-values from the integers. LINKS Table of n, a(n) for n=5..85. T. Piezas, "More on e^(pi*sqrt(163))" on sci.math.research, April 13, 2008 and The Ramanujan Pages EXAMPLE We have e^(Pi sqrt(19))-744 = (12(x^2-1))^3 with x = 2.9999998883... = 3 - 1/8954017.533..., therefore a(19) = 8954018. In the same way, e^(Pi sqrt(163))-744 = (12(x^2-1))^3 with x = 230.999999999999999999999999999890... = 231 - 1/9093255353570474976233448828.20..., thus a(163) = 9093255353570474976233448828. PROG (PARI) default(realprecision, 200); A138851(n)={ n=frac( sqrt( sqrtn( exp( sqrt(n)*Pi )-744, 3)/12 + 1 )); round( 1/(round(n)-n)) } CROSSREFS Cf. A003173, A014708, A056581 and references therein. Sequence in context: A117462 A155462 A109496 * A181061 A329934 A269611 Adjacent sequences: A138848 A138849 A138850 * A138852 A138853 A138854 KEYWORD sign AUTHOR M. F. Hasler, Apr 16 2008 STATUS approved

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)