A353201 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.

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, 9, 6, 17, 8, 51, 6, 35, 60, 31, 34, 9, 12, 31, 10, 15, 36, 30, 42, 33, 24, 45, 30, 12, 28, 51, 30, 11, 20, 21, 18, 33, 12, 31, 34, 15, 8, 15, 102, 65, 12, 9, 70, 93, 60, 63, 62, 42, 68

Offset: 1

Author

William Boyles, Jun 22 2022

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• William Boyles, Table of n, a(n) for n = 1..2500