A353201 - OEIS

%I #33 Aug 06 2022 08:27:11

%S 1,2,3,4,3,6,5,4,15,6,9,12,7,10,6,8,6,30,17,12,5,18,21,12,15,14,15,20,

%T 9,6,17,8,51,6,35,60,31,34,9,12,31,10,15,36,30,42,33,24,45,30,12,28,

%U 51,30,11,20,21,18,33,12,31,34,15,8,15,102,65,12,9,70,93,60,63,62,42,68

%N a(n) = smallest m such that f(m,x) is divisible by g(n,x), where f(m,x) = U(m-1,x/2), and U(k,x) is the k-th Chebyshev polynomial of the second kind over the field GF(2); g(n,x) is the polynomial over GF(2) whose coefficients correspond to the binary digits of n.

%C g(n,x) divides f(m,x) if and only if m is a multiple of a(n).

%H William Boyles, <a href="/A353201/b353201.txt">Table of n, a(n) for n = 1..2500</a>

%e For n=13, g(13,x) = 1*x^3 + 1*x^2 + 0*x + 1 because 13 is 1101 in binary. f(7,x) is the smallest that is divisible by g(13,x), so a(13) = 7.

%K nonn

%O 1,2

%A _William Boyles_, Jun 22 2022