A138852 Round(1/(x-round(x))), where x=(log(744+(12(p^2-1))^3)/Pi)^2, round(x) = nearest integer to x.

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

Offset

1,1

Comments

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.

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(3^2-1))^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...

Prog

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

Crossrefs

Cf. A139388, A138851, A003173, A014708, A056581 and references therein.

Sequence in context: A266198 A274990 A079236 * A062701 A341805 A252783

Adjacent sequences: A138849 A138850 A138851 * A138853 A138854 A138855

Keyword

sign

Author

M. F. Hasler, Apr 17 2008

Status

approved