A227062 Numbers whose base-5 sum of digits is 5.

9, 13, 17, 21, 29, 33, 37, 41, 45, 53, 57, 61, 65, 77, 81, 85, 101, 105, 129, 133, 137, 141, 145, 153, 157, 161, 165, 177, 181, 185, 201, 205, 225, 253, 257, 261, 265, 277, 281, 285, 301, 305, 325, 377, 381, 385, 401, 405, 425, 501, 505, 525, 629, 633, 637

Offset: 1

Author

Tom Edgar, Sep 01 2013

Keywords

• nonn
• base
• easy

Comments

All of the entries are odd.

Subsequence of A016813. - 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 5-ary expansion of 9 is (1,4), which has sum of digits 5.
The 5-ary expansion of 53 is (2,0,3), which has sum of digits 5.
10 is not on the list since the 5-ary expansion of 10 is (2,0), which has sum of digits 2 not 5.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..11613 (all terms with <= 15 base-5 digits)

Crossrefs

Cf. A018900, A187813.

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

Programs

Mathematica

Select[Range@ 640, Total@ IntegerDigits[#, 5] == 5 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI

select( is(n)=sumdigits(n,5)==5, [1..999]) \\ M. F. Hasler, Dec 23 2016

Python

from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits_base5):
    alst = []
    for d in range(2, maxdigits_base5 + 1):
        fulldigset = list("0"*(d-2) + "111112234")
        for firstdig in "1234":
            target_sum, restdigset = 5 - int(firstdig), fulldigset[:]
            restdigset.remove(firstdig)
            for p in multiset_permutations(restdigset, d-1):
                if sum(map(int, p)) == target_sum:
                  alst.append(int(firstdig+"".join(p), 5))
                  if int(p[0]) == target_sum:
                      break
    return alst
print(auptodigs(5)) # Michael S. Branicky, Sep 13 2021

Python

agen = A226636gen(sod=5, base=5) # 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=5))==5]