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A276233
a(n) = (n+256)/gcd(n,256).
2
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
1,1
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
Cf. A276234 (denominators).
Sequence in context: A051333 A273775 A182912 * A252726 A260679 A043676
KEYWORD
nonn
AUTHOR
Artur Jasinski, Aug 24 2016
STATUS
approved