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%I #6 Mar 31 2012 13:48:25
%S 2,-4,1435303,-2,4,4,-6,17,952364958135,-3,4,-2,-5,-8,-7,-4,-2,4,-10,
%T 2,21119108989115042,2,-8,4,-2,-7,10,3,2,-3,-4,-6,-10,-16,-19,-16,-11,
%U -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
%N Round(1/(x-round(x))), where x=(log(744+(12(p^2-1))^3)/Pi)^2, round(x) = nearest integer to x.
%C 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.
%H T. Piezas, <a href="http://groups.google.gp/group/sci.math.research/browse_thread/thread/3d24137c9a860893">"More on e^(pi*sqrt(163))" on sci.math.research, Apr 13, 2008</a> and his <a href="http://sites.google.com/site/tpiezas/ramanujan">Ramanujan Pages</a>
%e 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...
%e 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...
%o (PARI) default(realprecision,200); A138852(n)={ n=(log(744+(12*(n^2-1))^3)/Pi)^2; round(1/(x-round(x))) }
%Y Cf. A139388, A138851, A003173, A014708, A056581 and references therein.
%K sign
%O 1,1
%A _M. F. Hasler_, Apr 17 2008
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