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URL: https://oeis.org/A385552

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A385552
Period of {binomial(N,n) mod 5: N in Z}.
6
1, 5, 5, 5, 5, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125
OFFSET
0,2
COMMENTS
a(n) is the smallest power of 5 > n. For the general result, see A349593.
Since the modulus (5) is a prime, the remainder of binomial(N,n) is given by Lucas's theorem.
LINKS
EXAMPLE
For N == 0, 1, ..., 24 (mod 5), binomial(N,5) == {0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4} (mod 5).
PROG
(PARI) a(n) = if(n, 5^(logint(n, 5)+1), 1)
(Python)
from sympy import integer_log
def A385552(n): return 5*5**(integer_log(n, 5)[0]) if n else 1 # Chai Wah Wu, Jul 06 2025
CROSSREFS
Column 5 of A349593. A062383, A064235 (if offset 0), A385553, and A385554 are respectively columns 2, 3, 6, and 10.
Sequence in context: A282209 A082476 A365492 * A024729 A046271 A341600
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Jul 03 2025
STATUS
approved