A309958 Product of digits of (n written in base 7).

0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 2, 4, 6, 8, 10, 12, 0, 3, 6, 9, 12, 15, 18, 0, 4, 8, 12, 16, 20, 24, 0, 5, 10, 15, 20, 25, 30, 0, 6, 12, 18, 24, 30, 36, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 2, 4, 6, 8, 10, 12, 0, 3, 6, 9, 12, 15, 18, 0, 4, 8, 12, 16, 20, 24, 0, 5, 10, 15, 20, 25, 30, 0, 6, 12, 18, 24, 30, 36, 0, 0, 0

Offset: 0

Author

Ilya Gutkovskiy, Aug 24 2019

Keywords

• nonn
• base

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Product of digits of (n written in base k): A309953 (k = 3), A309954 (k = 4), A309956 (k = 5), A309957 (k = 6), this sequence (k = 7), A309959 (k = 8), A309788 (k = 9), A007954 (k = 10).

Cf. A007093, A053828.

Programs

Magma

[0] cat [&*Intseq(n,7):n in [1..100]]; // Marius A. Burtea, Aug 25 2019

Mathematica

Table[Times @@ IntegerDigits[n, 7], {n, 0, 100}]

PARI

a(n) = my(v=vecprod(digits(n, 7))); n>0 && return(v) \\ Felix Fröhlich, Sep 09 2019

Formula

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5) * (1 + A(x^7)).