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A284324 Numbers n such that product of digits of n is a power of 8. 5
1, 8, 11, 18, 24, 42, 81, 88, 111, 118, 124, 142, 181, 188, 214, 222, 241, 248, 284, 412, 421, 428, 444, 482, 811, 818, 824, 842, 881, 888, 1111, 1118, 1124, 1142, 1181, 1188, 1214, 1222, 1241, 1248, 1284, 1412, 1421, 1428, 1444, 1482, 1811, 1818, 1824, 1842 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Supersequence of A213084.

There are (2 + 4^d)/3 terms with d digits, for each d >= 1. - Robert Israel, Mar 31 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

1111 is in the sequence because 1*1*1*1 = 1 = 8^0.

MAPLE

dmax:= 4: # to get all terms with at most dmax digits

B[0, 1]:= {1, 8}:

B[1, 1]:= {2}:

B[2, 1]:= {4}:

for d from 2 to dmax do

  for j from 0 to 2 do

    B[j, d]:= map(t -> (10*t+1, 10*t+8), B[j, d-1])

        union map(t -> 10*t+4, B[(j+1) mod 3, d-1])

        union map(t->10*t+2, B[(j+2) mod 3, d-1])

od od:

seq(op(sort(convert(B[0, d], list))), d=1..dmax); # Robert Israel, Mar 31 2017

PROG

(MAGMA) Set(Sort([n: n in [1..10000], k in [0..20] | &*Intseq(n) eq 8^k]))

CROSSREFS

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).

Sequence in context: A306277 A067469 A237767 * A205856 A318079 A000852

Adjacent sequences:  A284321 A284322 A284323 * A284325 A284326 A284327

KEYWORD

nonn,base

AUTHOR

Jaroslav Krizek, Mar 26 2017

STATUS

approved

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Last modified September 21 22:07 EDT 2019. Contains 327283 sequences. (Running on oeis4.)