

A138852


Round(1/(xround(x))), where x=(log(744+(12(p^21))^3)/Pi)^2, round(x) = nearest integer to x.


2



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

1,1


COMMENTS

Related to almostinteger values of e^(pi sqrt n), obtained for larger Heegener numbers (A003173): T. Piezas draws attention on the fact that the wellknown integers very close to exp(pi sqrt(n)) are of the form (12(k^21))^3+744. Here this is expressed as the (rounded value) of the reciprocal of the (signed) distance from the integers of the nvalue corresponding to a given integer kvalue. As expected, records are obtained for k=3,9,21,231.


LINKS

Table of n, a(n) for n=1..75.
T. Piezas, "More on e^(pi*sqrt(163))" on sci.math.research, Apr 13, 2008 and his Ramanujan Pages


EXAMPLE

We have a(3) = 1435303 since (12(3^21))^3+744 = e^(pi sqrt(x)) with x = 19.0000006967... = 19+1/1435302.8.3...
In the same way, a(231)=43072298941682041177938098750 since (12(231^21))^3+744 = e^(pi sqrt(x)) with x = 163.0000000000000000000000000000232 = 163+1/43072298941682041177938098749.8977...


PROG

(PARI) default(realprecision, 200); A138852(n)={ n=(log(744+(12*(n^21))^3)/Pi)^2; round(1/(xround(x))) }


CROSSREFS

Cf. A139388, A138851, A003173, A014708, A056581 and references therein.
Sequence in context: A266198 A274990 A079236 * A062701 A252783 A192225
Adjacent sequences: A138849 A138850 A138851 * A138853 A138854 A138855


KEYWORD

sign


AUTHOR

M. F. Hasler, Apr 17 2008


STATUS

approved



