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

%I A227062 #27 Jul 10 2022 13:23:58
%S A227062 9,13,17,21,29,33,37,41,45,53,57,61,65,77,81,85,101,105,129,133,137,
%T A227062 141,145,153,157,161,165,177,181,185,201,205,225,253,257,261,265,277,
%U A227062 281,285,301,305,325,377,381,385,401,405,425,501,505,525,629,633,637
%N A227062 Numbers whose base-5 sum of digits is 5.
%C A227062 All of the entries are odd.
%C A227062 Subsequence of A016813. - _Michel Marcus_, Sep 03 2013
%C A227062 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
%H A227062 Michael S. Branicky, <a href="/A227062/b227062.txt">Table of n, a(n) for n = 1..11613</a> (all terms with <= 15 base-5 digits)
%e A227062 The 5-ary expansion of 9 is (1,4), which has sum of digits 5.
%e A227062 The 5-ary expansion of 53 is (2,0,3), which has sum of digits 5.
%e A227062 10 is not on the list since the 5-ary expansion of 10 is (2,0), which has sum of digits 2 not 5.
%t A227062 Select[Range@ 640, Total@ IntegerDigits[#, 5] == 5 &] (* _Michael De Vlieger_, Dec 23 2016 *)
%o A227062 (Sage) [i for i in [0..1000] if sum(Integer(i).digits(base=5))==5]
%o A227062 (PARI) select( is(n)=sumdigits(n,5)==5, [1..999]) \\ _M. F. Hasler_, Dec 23 2016
%o A227062 (Python)
%o A227062 from sympy.utilities.iterables import multiset_permutations
%o A227062 def auptodigs(maxdigits_base5):
%o A227062     alst = []
%o A227062     for d in range(2, maxdigits_base5 + 1):
%o A227062         fulldigset = list("0"*(d-2) + "111112234")
%o A227062         for firstdig in "1234":
%o A227062             target_sum, restdigset = 5 - int(firstdig), fulldigset[:]
%o A227062             restdigset.remove(firstdig)
%o A227062             for p in multiset_permutations(restdigset, d-1):
%o A227062                 if sum(map(int, p)) == target_sum:
%o A227062                   alst.append(int(firstdig+"".join(p), 5))
%o A227062                   if int(p[0]) == target_sum:
%o A227062                       break
%o A227062     return alst
%o A227062 print(auptodigs(5)) # _Michael S. Branicky_, Sep 13 2021
%o A227062 (Python)
%o A227062 agen = A226636gen(sod=5, base=5) # generator of terms using code in A226636
%o A227062 print([next(agen) for n in range(1, 56)]) # _Michael S. Branicky_, Jul 10 2022
%Y A227062 Cf. A018900, A187813.
%Y A227062 Cf. A226636 (b = 3), A226969 (b = 4), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10).
%K A227062 nonn,base,easy
%O A227062 1,1
%A A227062 _Tom Edgar_, Sep 01 2013