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
Jianing Song, Table of n, a(n) for n = 0..625
Wikipedia, Lucas's theorem
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
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Jul 03 2025
STATUS
approved
