A227080 Numbers whose base-6 sum of digits is 6.

11, 16, 21, 26, 31, 41, 46, 51, 56, 61, 66, 76, 81, 86, 91, 96, 111, 116, 121, 126, 146, 151, 156, 181, 186, 221, 226, 231, 236, 241, 246, 256, 261, 266, 271, 276, 291, 296, 301, 306, 326, 331, 336, 361, 366, 396, 436, 441, 446, 451, 456, 471, 476, 481, 486

Offset: 1

Author

Tom Edgar, Sep 01 2013

Keywords

• nonn
• base

Comments

Subsequence of A016861. - Michel Marcus, Sep 03 2013

In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016

Examples

			The 6-ary expansion of 11 is (1,5), which has sum of digits 6.
The 6-ary expansion of 46 is (1,1,4), which has sum of digits 6.
9 is not on the list since the 6-ary expansion of 10 is (1,3), which has sum of digits 4 not 6.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A018900, A187813.

Cf. A226636 (b = 3), A226639 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10).

Programs

Mathematica

Select[Range[500],Total[IntegerDigits[#,6]]==6&] (* Harvey P. Dale, Nov 25 2016 *)

PARI

select( is(n)=sumdigits(n,6)==6, [1..999]) \\ M. F. Hasler, Dec 23 2016

Python

# see A052224 for a faster version if going to high numbers
from sympy.ntheory import digits
def ok(n): return sum(digits(n, 6)[1:]) == 6
print([k for k in range(487) if ok(k)]) # Michael S. Branicky, Nov 16 2021

Python

agen = A226636gen(sod=6, base=6) # generator of terms using code in A226636
print([next(agen) for n in range(1, 56)]) # Michael S. Branicky, Jul 10 2022

Sage

[i for i in [0..1000] if sum(Integer(i).digits(base=6))==6]