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

Author

Jaroslav Krizek, Mar 25 2017

Keywords

• nonn
• base

Comments

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

Prime terms are in A020454.

Links

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

Crossrefs

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).

Programs

Magma

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

Mathematica

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

Python

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