A284295 -id:A284295 - cp's OEIS frontend

A284324 Numbers k such that product of digits of k 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

Jaroslav Krizek, Mar 26 2017

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

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

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

Supersequence of A213084.

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).

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

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

A284375 Numbers whose product of digits is a power of 0.

Original entry on oeis.org

0, 1, 10, 11, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 301, 302, 303

Offset: 1

Jaroslav Krizek, Mar 26 2017

			111 is in the sequence because 1*1*1 = 1 = 0^0.

Union of A011540 and A002275. Supersequence of A007088.

Cf. Numbers n such that product of digits of n is a power of k for k = 0 - 9: this sequence (k = 0), A002275 (k = 1), A028846 (k = 2), A174813 (k = 3), A284323 (k = 4), A276037 (k = 5), A276038 (k = 6), A276039 (k = 7), A284324 (k = 8), A284295 (k = 9), A328560 (k = 10).

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

Select[Range[0, 500], Times@@ IntegerDigits[#] <2 &] (* Indranil Ghosh, Mar 26 2017 *)

A284294 Numbers using only digits 1 and 9.

Original entry on oeis.org

1, 9, 11, 19, 91, 99, 111, 119, 191, 199, 911, 919, 991, 999, 1111, 1119, 1191, 1199, 1911, 1919, 1991, 1999, 9111, 9119, 9191, 9199, 9911, 9919, 9991, 9999, 11111, 11119, 11191, 11199, 11911, 11919, 11991, 11999, 19111, 19119, 19191, 19199, 19911, 19919

Offset: 1

Jaroslav Krizek, Mar 25 2017

Product of digits of terms is a power of 9; subsequence of A284295.

Prime terms are in A020457.

Alois P. Heinz, Table of n, a(n) for n = 1..16382

Cf. Numbers using only digits 1 and k for k = 0 and k = 2 - 9: A007088 (k = 0), A007931 (k = 2), A032917 (k = 3), A032822 (k = 4) , A276037 (k = 5), A284293 (k = 6), A276039 (k = 7), A213084 (k = 8), this sequence (k = 9).

[n: n in [1..20000] | Set(IntegerToSequence(n, 10)) subset {1, 9}];

Join @@ (FromDigits /@ Tuples[{1,9}, #] & /@ Range[5]) (* Giovanni Resta, Mar 25 2017 *)

The sum of first 2^n terms is (5*20^n + 38*10^n - 95*2^n + 1420)/171. - Giovanni Resta, Mar 25 2017

A284323 Numbers k such that product of digits of k is a power of 4.

Original entry on oeis.org

1, 4, 11, 14, 22, 28, 41, 44, 82, 88, 111, 114, 122, 128, 141, 144, 182, 188, 212, 218, 221, 224, 242, 248, 281, 284, 411, 414, 422, 428, 441, 444, 482, 488, 812, 818, 821, 824, 842, 848, 881, 884, 1111, 1114, 1122, 1128, 1141, 1144, 1182, 1188, 1212, 1218

Offset: 0

Jaroslav Krizek, Mar 25 2017

			1111 is in the sequence because 1*1*1*1 = 1 = 4^0.

Supersequence of A032822.

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), this sequence (k = 4), A276037 (k = 5), A276038 (k = 6), A276039 (k = 7), A284324 (k = 8), A284295 (k = 9).

Set(Sort([n: n in [1..10000], k in [0..20] | &*Intseq(n) eq 4^k]));

FromDigits /@ Select[Join @@ Map[Tuples[2^Range[0, 3], #] &, Range@ 4], IntegerQ@ Log[4, Times @@ #] &] (* Michael De Vlieger, Mar 25 2017 *)

A316315 Numbers k such that the product of digits of k is a power of 12.

Original entry on oeis.org

1, 11, 26, 34, 43, 62, 111, 126, 134, 143, 162, 216, 223, 232, 261, 289, 298, 314, 322, 341, 368, 386, 413, 431, 449, 466, 494, 612, 621, 638, 646, 664, 683, 829, 836, 863, 892, 928, 944, 982, 1111, 1126, 1134, 1143, 1162, 1216, 1223, 1232, 1261, 1289, 1298

Offset: 1

Isaac Weiss and Henry Potts-Rubin, Jun 29 2018

			466 is in the sequence because 4*6*6 = 144 = 12^2.

Alois P. Heinz, Table of n, a(n) for n = 1..64235

Cf. A284375, A002275, A028846, A174813, A284323, A276037, A276038, A276039, A284324, A284295, A328560.

FromDigits /@ Select[Join @@ Map[Tuples[{1, 2, 3, 4, 6, 8, 9}, #] &, Range@4], IntegerQ@Log[12, Times @@ #] &]

Two duplicate terms removed by Alois P. Heinz, Oct 20 2019

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

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A284375 Numbers whose product of digits is a power of 0.

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A284294 Numbers using only digits 1 and 9.

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A284323 Numbers k such that product of digits of k is a power of 4.

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A316315 Numbers k such that the product of digits of k is a power of 12.

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