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

1,2

Comments

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

Links

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

Example

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.

Crossrefs

Sequence in context: A186970 A064380 A290732 * A229110 A229949 A126214

Adjacent sequences: A353198 A353199 A353200 * A353202 A353203 A353204

Keyword

nonn

Author

William Boyles, Jun 22 2022

Status

approved