A391959 Second column of A391957.

0, 0, 0, 5, 3, 1, 10, 6, 2, 32, 24, 16, 31, 21, 11, 30, 18, 6, 64, 48, 32, 57, 39, 21, 50, 30, 10, 149, 123, 97, 130, 102, 74, 111, 81, 51, 163, 129, 95, 138, 102, 66, 113, 75, 37, 177, 135, 93, 146, 102, 58, 115, 69, 23, 298, 246, 194, 255, 201, 147, 212, 156

Offset

0,4

Comments

Powers of 3 in the factorization of A391956.

The first 82 terms were obtained from a brute force calculation of A391956. From these results a regular pattern is observed to determine more terms.

See also A391957 for a Python program.

Links

A.H.M. Smeets, Table of n, a(n) for n = 0..10000

Formula

Conjectured: this sequence can be obtained by the following two rules:

(Eq.1) a(3^n) = 3*a(3^(n-1)) + 2*3^n - 1, a(1) = 0 (see also A392083) and

(Eq.2) a(n*3^m + 3^(m-1)*k) = a(n*3^m) + a(3^(m-1)) - 2*k*3^(m-1)*Sum_{i = 1..n} A051064(i), 0 < k < 3.

The second rule (Eq.2) is a generalization of formula like:

a(3*n+k) = a(3*n) - 2*k*Sum_{i = 1..n} A051064(i), 0 < k < 3.

a(9*n+3*k) = a(9*n) + 5 - 6*k*Sum_{i = 1..n} A051064(i+1), 0 < k < 3.

Crossrefs

Cf. A051064, A391956, A391957, A392084.

Sequence in context: A021192 A380793 A074396 * A383186 A229958 A157891

Adjacent sequences: A391956 A391957 A391958 * A391960 A391961 A391962

Keyword

nonn

Author

A.H.M. Smeets, Dec 28 2025

Status

approved