A138852 a(n) = round(1/(x-round(x))), where x = (log(744 + (12(n^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
Keywords
Examples
We have a(3) = 1435303 since (12(3^2-1))^3+744 = e^(pi sqrt(x)) with x = 19.0000006967... = 19 + 1/1435302.833... 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...
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Titus Piezas III, "More on e^(pi*sqrt(163))" on sci.math.research, Apr 13, 2008 and his Ramanujan Pages.
Programs
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Mathematica
a[n_] := Module[{x = (Log[744 + (12*(n^2-1))^3] / Pi)^2}, Round[1/(x - Round[x])]]; Array[a, 100] (* Amiram Eldar, Jan 17 2025 *) -
PARI
default(realprecision,200); A138852(n)={ n=(log(744+(12*(n^2-1))^3)/Pi)^2; round(1/(x-round(x))) }
Comments