login
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
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
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
KEYWORD
nonn
AUTHOR
William Boyles, Jun 22 2022
STATUS
approved