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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

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

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).

Sequence in context: A074197 A106673 A329389 * A131858 A258588 A371187

Adjacent sequences: A227077 A227078 A227079 * A227081 A227082 A227083

Keyword

nonn,base

Author

Tom Edgar, Sep 01 2013

Status

approved