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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

(Sage) [i for i in [0..1000] if sum(Integer(i).digits(base=5))==5]
(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

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).

Sequence in context: A050109 A294357 A329388 * A134441 A174055 A273059

Adjacent sequences: A227059 A227060 A227061 * A227063 A227064 A227065

Keyword

nonn,base,easy

Author

Tom Edgar, Sep 01 2013

Status

approved