A227238 Numbers whose base-9 sum of digits is 9.

17, 25, 33, 41, 49, 57, 65, 73, 89, 97, 105, 113, 121, 129, 137, 145, 153, 169, 177, 185, 193, 201, 209, 217, 225, 249, 257, 265, 273, 281, 289, 297, 329, 337, 345, 353, 361, 369, 409, 417, 425, 433, 441, 489, 497, 505, 513, 569, 577, 585, 649, 657, 737, 745

Offset: 1

Author

Tom Edgar, Sep 01 2013

Keywords

• nonn
• base
• easy

Comments

All of the entries are odd.

Subsequence of A017077. - Michel Marcus, Sep 02 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 9-ary expansion of 17 is (1,8), which has sum of digits 9.
The 9-ary expansion of 169 is (2,0,7), which has sum of digits 9.
10 is not on the list since the 9-ary expansion of 10 is (1,1), which has sum of digits 2 not 9.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A018900, A187813.

Cf. A226636 (b = 3), A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10).

Programs

Mathematica

Select[Range@ 750, Total@ IntegerDigits[#, 9] == 9 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI

select( is(n)=sumdigits(n,9)==9, [1..999]) \\ M. F. Hasler, Dec 23 2016

Python

agen = A226636gen(sod=9, base=9) # generator of terms using code in A226636
print([next(agen) for n in range(1, 55)]) # Michael S. Branicky, Jul 10 2022

Sage

[i for i in [0..1000] if sum(Integer(i).digits(base=9))==9]