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A309953 Product of digits of (n written in base 3).

%I A309953 #19 Mar 18 2024 11:21:43
%S A309953 0,1,2,0,1,2,0,2,4,0,0,0,0,1,2,0,2,4,0,0,0,0,2,4,0,4,8,0,0,0,0,0,0,0,
%T A309953 0,0,0,0,0,0,1,2,0,2,4,0,0,0,0,2,4,0,4,8,0,0,0,0,0,0,0,0,0,0,0,0,0,2,
%U A309953 4,0,4,8,0,0,0,0,4,8,0,8,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A309953 Product of digits of (n written in base 3).
%H A309953 Seiichi Manyama, <a href="/A309953/b309953.txt">Table of n, a(n) for n = 0..10000</a>
%F A309953 G.f. A(x) satisfies: A(x) = x * (1 + 2*x) * (1 + A(x^3)).
%p A309953 a:= proc(n) a(n):= `if`(n<3, n, irem(n, 3, 'q')*a(q)) end:
%p A309953 seq(a(n), n=0..100);  # _Alois P. Heinz_, Mar 18 2024
%t A309953 Table[Times @@ IntegerDigits[n, 3], {n, 0, 100}]
%o A309953 (PARI) a(n) = {if(n, vecprod(digits(n,3)), 0)} \\ _Andrew Howroyd_, Aug 24 2019
%o A309953 (Magma) [0] cat [&*Intseq(n,3):n in [1..100]]; // _Marius A. Burtea_, Aug 25 2019
%Y A309953 Cf. A007089, A007954, A053735.
%K A309953 nonn,base,look
%O A309953 0,3
%A A309953 _Ilya Gutkovskiy_, Aug 24 2019