A284294 -id:A284294 - 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

A284295 Numbers n such that product of digits of n is a power of 9.

Original entry on oeis.org

1, 9, 11, 19, 33, 91, 99, 111, 119, 133, 191, 199, 313, 331, 339, 393, 911, 919, 933, 991, 999, 1111, 1119, 1133, 1191, 1199, 1313, 1331, 1339, 1393, 1911, 1919, 1933, 1991, 1999, 3113, 3131, 3139, 3193, 3311, 3319, 3333, 3391, 3399, 3913, 3931, 3939, 3993

Offset: 1

Jaroslav Krizek, Mar 25 2017

Supersequence of A284294.

			1111 is in the sequence because 1*1*1*1 = 1 = 9^0.

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), A284324 (k = 8), this sequence (k = 9).

Set(Sort([n: n in [1..10000], k in [0..20] | &*Intseq(n) eq 9^k]))

FromDigits /@ Select[Join @@ Map[Tuples[{1, 3, 9}, #] &, Range@ 4], IntegerQ@ Log[9, Times @@ #] &] (* Michael De Vlieger, Mar 25 2017 *)

A213084 Numbers consisting of ones and eights.

Original entry on oeis.org

1, 8, 11, 18, 81, 88, 111, 118, 181, 188, 811, 818, 881, 888, 1111, 1118, 1181, 1188, 1811, 1818, 1881, 1888, 8111, 8118, 8181, 8188, 8811, 8818, 8881, 8888, 11111, 11118, 11181, 11188, 11811, 11818, 11881, 11888, 18111, 18118, 18181, 18188, 18811, 18818

Offset: 1

Jens Ahlström, Jun 05 2012

One and eight begin with vowels. The subsequence of primes begins 11, 181, 811, 1181, 1811, 8111. - Jonathan Vos Post, Jun 14 2012

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

Cf. A020456 (primes in this sequence).

Cf. numbers consisting of 1s and ks: A007088 (k=0), A007931 (k=2), A032917 (k=3), A032822 (k=4), A276037 (k=5), A284293 (k=6), A276039 (k=7), A284294 (k=9).

Flatten[Table[FromDigits/@Tuples[{1,8},n],{n,5}]] (* Harvey P. Dale, Aug 27 2014 *)

is(n) = #setintersect(vecsort(digits(n), , 8), [0, 2, 3, 4, 5, 6, 7, 9])==0 \\ Felix Fröhlich, Sep 09 2019

res = []
i = 0
while len (res) < 260:
    for c in str(i):
        if c in '18':
            continue
        else:
            break
    else:
        res.append(i)
    i = i + 1
print(res)

def a(n): return int(bin(n+1)[3:].replace('1', '8').replace('0', '1'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jun 26 2025

cp's OEIS Frontend

A284293 Numbers using only digits 1 and 6.

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A284295 Numbers n such that product of digits of n is a power of 9.

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A213084 Numbers consisting of ones and eights.

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