A276037 -id:A276037 - cp's OEIS frontend

A284294 Numbers using only digits 1 and 9.

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 *)

A284381 Numbers k with digits 5 and 8 only.

Original entry on oeis.org

5, 8, 55, 58, 85, 88, 555, 558, 585, 588, 855, 858, 885, 888, 5555, 5558, 5585, 5588, 5855, 5858, 5885, 5888, 8555, 8558, 8585, 8588, 8855, 8858, 8885, 8888, 55555, 55558, 55585, 55588, 55855, 55858, 55885, 55888, 58555, 58558, 58585, 58588, 58855, 58858

Offset: 1

Jaroslav Krizek, Mar 28 2017

All terms except the first are composite.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), this sequence (k = 8), A284382 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 8}];

Join @@ ((FromDigits /@ Tuples[{5, 8}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)

def a(n): return int(bin(n+1)[3:].replace('0', '5').replace('1', '8'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 08 2021

a(n) = (A284380(n)+A284382(n))/2. - Robert Israel, Mar 28 2017

A284382 Numbers k with digits 5 and 9 only.

Original entry on oeis.org

5, 9, 55, 59, 95, 99, 555, 559, 595, 599, 955, 959, 995, 999, 5555, 5559, 5595, 5599, 5955, 5959, 5995, 5999, 9555, 9559, 9595, 9599, 9955, 9959, 9995, 9999, 55555, 55559, 55595, 55599, 55955, 55959, 55995, 55999, 59555, 59559, 59595, 59599, 59955, 59959

Offset: 1

Jaroslav Krizek, Mar 28 2017

Prime terms are in A020468.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), A284381 (k = 8), this sequence (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 9}];

Join @@ ((FromDigits /@ Tuples[{5, 9}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)

def a(n): return int(bin(n+1)[3:].replace('0', '5').replace('1', '9'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 09 2021

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

A385324 Numbers whose digits are all powers of the same single-digit base.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 28, 31, 33, 39, 41, 42, 44, 48, 51, 55, 61, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 124, 128, 131, 133, 139, 141, 142, 144, 148

Offset: 1

Stefano Spezia, Jun 25 2025

			84 is a term since its digits 8 and 4 are both powers of 2.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Cf. A028846, A174813, A276037, A276039, A284293.

Cf. A385351 (subsequence)

Select[Range[0,148],SubsetQ[{0},dig=IntegerDigits[#]]||SubsetQ[{1,2,4,8},dig]||SubsetQ[{1,3,9},dig]||SubsetQ[{1,5},dig]||SubsetQ[{1,6},dig]||SubsetQ[{1,7},dig] &]

{0} U A028846 U A174813 U A276037 U A276039 U A284293.

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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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A284381 Numbers k with digits 5 and 8 only.

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A284382 Numbers k with digits 5 and 9 only.

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

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A385324 Numbers whose digits are all powers of the same single-digit base.

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