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A284324 Numbers k such that product of digits of k is a power of 8.

%I A284324 #18 Jun 25 2025 14:35:18
%S A284324 1,8,11,18,24,42,81,88,111,118,124,142,181,188,214,222,241,248,284,
%T A284324 412,421,428,444,482,811,818,824,842,881,888,1111,1118,1124,1142,1181,
%U A284324 1188,1214,1222,1241,1248,1284,1412,1421,1428,1444,1482,1811,1818,1824,1842
%N A284324 Numbers k such that product of digits of k is a power of 8.
%C A284324 There are (2 + 4^d)/3 terms with d digits, for each d >= 1. - _Robert Israel_, Mar 31 2017
%H A284324 Robert Israel, <a href="/A284324/b284324.txt">Table of n, a(n) for n = 1..10000</a>
%e A284324 1111 is in the sequence because 1*1*1*1 = 1 = 8^0.
%p A284324 dmax:= 4: # to get all terms with at most dmax digits
%p A284324 B[0,1]:= {1,8}:
%p A284324 B[1,1]:= {2}:
%p A284324 B[2,1]:= {4}:
%p A284324 for d from 2 to dmax do
%p A284324   for j from 0 to 2 do
%p A284324     B[j,d]:= map(t -> (10*t+1,10*t+8), B[j,d-1])
%p A284324         union map(t -> 10*t+4, B[(j+1) mod 3, d-1])
%p A284324         union map(t->10*t+2, B[(j+2) mod 3, d-1])
%p A284324 od od:
%p A284324 seq(op(sort(convert(B[0,d],list))),d=1..dmax); # _Robert Israel_, Mar 31 2017
%o A284324 (Magma) Set(Sort([n: n in [1..10000], k in [0..20] | &*Intseq(n) eq 8^k]));
%Y A284324 Supersequence of A213084.
%Y A284324 Cf. Numbers n such that product of digits of n is a power of k for k = 0 - 9: A284375 (k = 0), A002275 (k = 1), A028846 (k = 2), A174813 (k = 3), A284323 (k = 4), A276037 (k = 5), A276038 (k = 6), A276039 (k = 7), this sequence (k = 8), A284295 (k = 9).
%K A284324 nonn,base
%O A284324 1,2
%A A284324 _Jaroslav Krizek_, Mar 26 2017