OFFSET
1,1
LINKS
Ray Chandler, Table of n, a(n) for n = 1..1024
FORMULA
a(n) = numerator of 1+256/n, which is the limit of the function EllipticTheta(3, 0, q)^8 + EllipticTheta(2, 0, sqrt(q))^8/(n q) when q -> 0.
a(2k-1) = n + 256 = 2k-1 + 256 = 2k + 255
a(4k-2) = n/2 + 128 = 2k-1 + 128 = 2k + 127
a(8k-4) = n/4 + 64 = 2k-1 + 64 = 2k + 63
a(16k-8) = n/8 + 32 = 2k-1 + 32 = 2k + 31
a(32k-16) = n/16 + 16 = 2k-1 + 16 = 2k + 15
a(64k-32) = n/32 + 8 = 2k-1 + 8 = 2k + 7
a(128k-64) = n/64 + 4 = 2k-1 + 4 = 2k + 3
a(256k-128) = n/128 + 2 = 2k-1 + 2 = 2k + 1.
a(n) = 2*a(n-256) - a(n-512) for n > 512. - Ray Chandler, Aug 03 2023
MAPLE
seq((n+256)/igcd(n, 256), n=1..300); # Robert Israel, Aug 25 2016
MATHEMATICA
Numerator[Table[Limit[EllipticTheta[3, 0, b]^8 + EllipticTheta[2, 0, Sqrt[b]]^8/(n b), b -> 0], {n, 1, 50}]]
Table[(n + 256)/GCD[n, 256], {n, 60}] (* Ray Chandler, Aug 03 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Aug 24 2016
STATUS
approved