A385553 - OEIS

A385553

Period of {binomial(N,n) mod 6: N in Z}.

1, 6, 12, 36, 72, 72, 72, 72, 144, 432, 432, 432, 432, 432, 432, 432, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 2592, 2592, 2592, 2592, 2592, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184, 5184

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Jianing Song, Table of n, a(n) for n = 0..1024

FORMULA

a(n) = (the smallest power of 2 > n) * (the smallest power of 3 > n) = A062383(n) * A064235(n+1). For the general result, see A349593.

EXAMPLE

For N == 0, 1, ..., 35 (mod 36), binomial(N,3) == {0, 0, 0, 1, 4, 4, 2, 5, 2, 0, 0, 3, 4, 4, 4, 5, 2, 2, 0, 3, 0, 4, 4, 1, 2, 2, 2, 3, 0, 0, 4, 1, 4, 2, 2, 5} (mod 6).

For N == 0, 1, ..., 71 (mod 72), binomial(N,4) == {0, 0, 0, 0, 1, 5, 3, 5, 4, 0, 0, 0, 3, 1, 5, 3, 2, 4, 0, 0, 3, 3, 1, 5, 0, 2, 4, 0, 3, 3, 3, 1, 2, 0, 2, 4, 3, 3, 3, 3, 4, 2, 0, 2, 1, 3, 3, 3, 0, 4, 2, 0, 5, 1, 3, 3, 0, 0, 4, 2, 3, 5, 1, 3, 0, 0, 0, 4, 5, 3, 5, 1} (mod 6).

PROG

(PARI) a(n) = if(n, (2^(logint(n, 2)+1)) * (3^(logint(n, 3)+1)), 1)

(Python)

from sympy import integer_log

def A385553(n): return 3**(integer_log(n, 3)[0]+1)<<n.bit_length() if n else 1 # Chai Wah Wu, Nov 17 2025

CROSSREFS

Column 6 of A349593. A062383, A064235 (if offset 0), A385552, and A385554 are respectively columns 2, 3, 5, and 10.

Sequence in context: A376003 A212976 A352621 * A176681 A064476 A324483

Adjacent sequences: A385550 A385551 A385552 * A385554 A385555 A385556

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Jul 03 2025

STATUS

approved