This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385553 #13 Jul 06 2025 10:06:52
%S A385553 1,6,12,36,72,72,72,72,144,432,432,432,432,432,432,432,864,864,864,
%T A385553 864,864,864,864,864,864,864,864,2592,2592,2592,2592,2592,5184,5184,
%U A385553 5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184,5184
%N A385553 Period of {binomial(N,n) mod 6: N in Z}.
%H A385553 Jianing Song, <a href="/A385553/b385553.txt">Table of n, a(n) for n = 0..1024</a>
%F A385553 a(n) = (the smallest power of 2 > n) * (the smallest power of 3 > n) = A062383(n) * A064235(n+1). For the general result, see A349593.
%e A385553 For N == 0, 1, ..., 35 (mod 36), binomial(N,3) == {0, 0, 0, 1, 4, 4, 2, 5, 2, 0, 0, 3, 4, 4, 4, 5, 2, 2, 0, 3, 0, 4, 4, 1, 2, 2, 2, 3, 0, 0, 4, 1, 4, 2, 2, 5} (mod 6).
%e A385553 For N == 0, 1, ..., 71 (mod 72), binomial(N,4) == {0, 0, 0, 0, 1, 5, 3, 5, 4, 0, 0, 0, 3, 1, 5, 3, 2, 4, 0, 0, 3, 3, 1, 5, 0, 2, 4, 0, 3, 3, 3, 1, 2, 0, 2, 4, 3, 3, 3, 3, 4, 2, 0, 2, 1, 3, 3, 3, 0, 4, 2, 0, 5, 1, 3, 3, 0, 0, 4, 2, 3, 5, 1, 3, 0, 0, 0, 4, 5, 3, 5, 1} (mod 6).
%o A385553 (PARI) a(n) = if(n, (2^(logint(n,2)+1)) * (3^(logint(n,3)+1)), 1)
%Y A385553 Column 6 of A349593. A062383, A064235 (if offset 0), A385552, and A385554 are respectively columns 2, 3, 5, and 10.
%K A385553 nonn,easy
%O A385553 0,2
%A A385553 _Jianing Song_, Jul 03 2025