A213084 -id:A213084 - cp's OEIS frontend

A284293 Numbers using only digits 1 and 6.

1, 6, 11, 16, 61, 66, 111, 116, 161, 166, 611, 616, 661, 666, 1111, 1116, 1161, 1166, 1611, 1616, 1661, 1666, 6111, 6116, 6161, 6166, 6611, 6616, 6661, 6666, 11111, 11116, 11161, 11166, 11611, 11616, 11661, 11666, 16111, 16116, 16161, 16166, 16611, 16616

Offset: 1

Jaroslav Krizek, Mar 25 2017

Product of digits of n is a power of 6; subsequence of A276038.

Prime terms are in A020454.

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), this sequence (k = 6), A276039 (k = 7), A213084 (k = 8), A284294 (k = 9).

[n: n in [1..20000] | Set(IntegerToSequence(n, 10)) subset {1, 6}];

Join @@ (FromDigits /@ Tuples[{1,6}, #] & /@ Range[5]) (* Giovanni Resta, Mar 25 2017 *)

def A284293(n): return 5*int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1)//9 # Chai Wah Wu, Jun 28 2025

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

Original entry on oeis.org

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

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

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A284293 Numbers using only digits 1 and 6.

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

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A284294 Numbers using only digits 1 and 9.

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