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

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

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