cp's OEIS Frontend

A354410 Numbers with as many zeros as the sum of their digits.

%I A354410 #33 Jan 12 2023 18:31:55
%S A354410 10,200,1001,1010,1100,3000,10002,10020,10200,12000,20001,20010,20100,
%T A354410 21000,40000,100003,100011,100030,100101,100110,100300,101001,101010,
%U A354410 101100,103000,110001,110010,110100,111000,130000,200002,200020,200200,202000,220000
%N A354410 Numbers with as many zeros as the sum of their digits.
%C A354410 As is normal, there are no leading zeros. The places of k zeros and the nonzero digits that are partitions of k are combinatorial.
%C A354410 Numbers k such that A007953(k) = A055641(k). - _Felix Fröhlich_, May 26 2022
%H A354410 Rémy Sigrist, <a href="/A354410/a354410.gp.txt">PARI program</a>
%t A354410 Select[Range[250000],DigitCount[#,10,0]==Total[IntegerDigits[#]]&] (* _Harvey P. Dale_, Jan 12 2023 *)
%o A354410 (PARI) isok(m) = my(d=digits(m)); vecsum(d) == #select(x->(x==0), d); \\ _Michel Marcus_, May 26 2022
%o A354410 (PARI) See Links section.
%o A354410 (Python) # after linked PARI by _Rémy Sigrist_
%o A354410 base, vv, nb = 10, [0], 0
%o A354410 def visit(v, s, z, r):
%o A354410     global base, vv, nb
%o A354410     if v and s==z:
%o A354410         nb += 1
%o A354410         if nb > len(vv): vv.append(len(vv))
%o A354410         vv[nb-1] = v
%o A354410     if s-z-r <= 0 and s-z+(base-1)*r >= 0:
%o A354410         if v: visit(base*v, s, z+1, r-1)
%o A354410         for d in range(1, base): visit(base*v+d, s+d, z, r-1)
%o A354410 def auptod(digits): visit(0, 0, 0, digits); return sorted(set(vv))
%o A354410 print(auptod(6)) # _Michael S. Branicky_, May 26 2022
%Y A354410 Subsequence of A011540.
%Y A354410 Cf. A007953 (sum of digits), A055641 (number of 0's).
%Y A354410 Cf. A031443, A061384.
%K A354410 nonn,base
%O A354410 1,1
%A A354410 _Tamas Sandor Nagy_, May 25 2022