A276233 - OEIS

%I #35 Aug 03 2023 15:23:09

%S 257,129,259,65,261,131,263,33,265,133,267,67,269,135,271,17,273,137,

%T 275,69,277,139,279,35,281,141,283,71,285,143,287,9,289,145,291,73,

%U 293,147,295,37,297,149,299,75,301,151,303,19,305,153

%N a(n) = (n+256)/gcd(n,256).

%H Ray Chandler, <a href="/A276233/b276233.txt">Table of n, a(n) for n = 1..1024</a>

%H <a href="/index/Rec#order_512">Index entries for linear recurrences with constant coefficients</a>, order 512.

%F 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.

%F a(2k-1) = n + 256 = 2k-1 + 256 = 2k + 255

%F a(4k-2) = n/2 + 128 = 2k-1 + 128 = 2k + 127

%F a(8k-4) = n/4 + 64 = 2k-1 + 64 = 2k + 63

%F a(16k-8) = n/8 + 32 = 2k-1 + 32 = 2k + 31

%F a(32k-16) = n/16 + 16 = 2k-1 + 16 = 2k + 15

%F a(64k-32) = n/32 + 8 = 2k-1 + 8 = 2k + 7

%F a(128k-64) = n/64 + 4 = 2k-1 + 4 = 2k + 3

%F a(256k-128) = n/128 + 2 = 2k-1 + 2 = 2k + 1.

%F a(n) = 2*a(n-256) - a(n-512) for n > 512. - _Ray Chandler_, Aug 03 2023

%p seq((n+256)/igcd(n,256),n=1..300); # _Robert Israel_, Aug 25 2016

%t Numerator[Table[Limit[EllipticTheta[3, 0, b]^8 + EllipticTheta[2, 0,Sqrt[b]]^8/(n b),b -> 0], {n, 1, 50}]]

%t Table[(n + 256)/GCD[n, 256], {n, 60}] (* _Ray Chandler_, Aug 03 2023 *)

%Y Cf. A276234 (denominators).

%K nonn

%O 1,1

%A _Artur Jasinski_, Aug 24 2016