A385554 Period of {binomial(N,n) mod 10: N in Z}.

1, 10, 20, 20, 40, 200, 200, 200, 400, 400, 400, 400, 400, 400, 400, 400, 800, 800, 800, 800, 800, 800, 800, 800, 800, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000, 8000

Offset: 0

Author

Jianing Song, Jul 03 2025

Keywords

• nonn
• easy

Examples

			For N == 0, 1, ..., 19 (mod 20), binomial(N,3) == {0, 0, 0, 1, 4, 0, 0, 5, 6, 4, 0, 5, 0, 6, 4, 5, 0, 0, 6, 9} (mod 10).
For N == 0, 1, ..., 39 (mod 40), binomial(N,4) == {0, 0, 0, 0, 1, 5, 5, 5, 0, 6, 0, 0, 5, 5, 1, 5, 0, 0, 0, 6, 5, 5, 5, 5, 6, 0, 0, 0, 5, 1, 5, 5, 0, 0, 6, 0, 5, 5, 5, 1} (mod 10).
		

Links

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

Crossrefs

Column 10 of A349593. A062383, A064235 (if offset 0), A385552, and A385553 are respectively columns 2, 3, 5, and 6.

Programs

PARI

a(n) = if(n, (2^(logint(n,2)+1)) * (5^(logint(n,5)+1)), 1)

Formula

a(n) = (the smallest power of 2 > n) * (the smallest power of 5 > n) = A062383(n) * A385552(n). For the general result, see A349593.