A309788 Product of digits of (n written in base 9).

0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 2, 4, 6, 8, 10, 12, 14, 16, 0, 3, 6, 9, 12, 15, 18, 21, 24, 0, 4, 8, 12, 16, 20, 24, 28, 32, 0, 5, 10, 15, 20, 25, 30, 35, 40, 0, 6, 12, 18, 24, 30, 36, 42, 48, 0, 7, 14, 21, 28, 35, 42, 49, 56, 0, 8, 16, 24, 32, 40, 48, 56, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 2

Offset: 0

Author

Ilya Gutkovskiy, Aug 26 2019

Keywords

• nonn
• base
• look

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), A309958 (k = 7), A309959 (k = 8), this sequence (k = 9), A007954 (k = 10).

Cf. A007095, A053830.

Programs

Magma

[0] cat [&*Intseq(n,9):n in [1..100]]; // Marius A. Burtea, Aug 26 2019

Mathematica

Table[Times @@ IntegerDigits[n, 9], {n, 0, 100}]

Formula

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7) * (1 + A(x^9)).