A374959 a(n) is the least k such that binomial(A349958(n), k) is a multiple of n.

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 2, 4, 1, 3, 1, 2, 1, 2, 1, 3, 1, 1, 3, 2, 3, 2, 1, 4, 2, 3, 1, 3, 1, 3, 2, 8, 1, 5, 1, 2, 2, 6, 1, 4, 2, 3, 2, 2, 1, 3, 1, 2, 4, 1, 4, 4, 1, 2, 6, 4, 1, 5, 1, 2, 2, 4, 5, 2, 1, 3, 1, 2, 1, 3, 3, 4, 3

Offset: 1

Author

Rémy Sigrist, Jul 25 2024

Keywords

• nonn

Examples

			For n = 12: the first multiple of 12 in Pascal's triangle appears in row 9; this row contains: 1, 9, 36, 84, 126, 126, 84, 36, 9, 1; the first multiple of 12 (36), appears at (0-based) index 2; so a(12) = 2.
		

Crossrefs

Cf. A007318, A349958, A357327.

Programs

PARI

a(n) = { my (r = [1 % n], j); for (i = 0, oo, if (vecmin(r, &j)==0, return (j-1), r = (concat(0, r) + concat(r, 0)) % n;);); }

Python

from math import comb
def A374959(n): return next(k for j in range(n+1) for k in range(j+1) if not (comb(j,k) % n)) # Chai Wah Wu, Jul 30 2024