A109642 a(n) = least composite m such that binomial(3m,m) mod m = 3^n.

4, 15, 57, 765, 1025, 2097, 4947, 9189, 103599, 216927, 4346128, 1558269, 1977777, 208510373, 14493123, 493262541, 144228033

Offset

1,1

Comments

Subsequence of A109641.

Links

Table of n, a(n) for n=1..17.

Mathematica

In[1]:= n = 1; Do[If[ !PrimeQ[k] && Mod[Binomial[3*k, k], k] == 3^n, Print[k]; n++ ], {k, 1, 10^4}]

Prog

(Python)
from itertools import count
from sympy import isprime
from oeis_sequences.OEISsequences import binom_mod
def A109642(n):
    k = 3**n
    for m in count(k):
        if not isprime(m) and binom_mod(3*m, m, m)==k:
            return m # Chai Wah Wu, Jan 13 2026

Crossrefs

Cf. A080469, A109641.

Sequence in context: A371777 A095930 A026850 * A307570 A164589 A377315

Adjacent sequences: A109639 A109640 A109641 * A109643 A109644 A109645

Keyword

nonn,more

Author

Ryan Propper, Aug 05 2005

Extensions

Edited by Max Alekseyev, Nov 03 2009

a(14)-a(17) from Chai Wah Wu, Jul 30 2025

Status

approved