A276233 a(n) = (n+256)/gcd(n,256).

257, 129, 259, 65, 261, 131, 263, 33, 265, 133, 267, 67, 269, 135, 271, 17, 273, 137, 275, 69, 277, 139, 279, 35, 281, 141, 283, 71, 285, 143, 287, 9, 289, 145, 291, 73, 293, 147, 295, 37, 297, 149, 299, 75, 301, 151, 303, 19, 305, 153

Offset: 1

Author

Artur Jasinski, Aug 24 2016

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..1024
• Index entries for linear recurrences with constant coefficients, order 512.

Crossrefs

Cf. A276234 (denominators).

Programs

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 *)

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