A354410 - OEIS

%I #33 Jan 12 2023 18:31:55

%S 10,200,1001,1010,1100,3000,10002,10020,10200,12000,20001,20010,20100,

%T 21000,40000,100003,100011,100030,100101,100110,100300,101001,101010,

%U 101100,103000,110001,110010,110100,111000,130000,200002,200020,200200,202000,220000

%N Numbers with as many zeros as the sum of their digits.

%C 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 Numbers k such that A007953(k) = A055641(k). - _Felix Fröhlich_, May 26 2022

%H Rémy Sigrist, <a href="/A354410/a354410.gp.txt">PARI program</a>

%t Select[Range[250000],DigitCount[#,10,0]==Total[IntegerDigits[#]]&] (* _Harvey P. Dale_, Jan 12 2023 *)

%o (PARI) isok(m) = my(d=digits(m)); vecsum(d) == #select(x->(x==0), d); \\ _Michel Marcus_, May 26 2022

%o (PARI) See Links section.

%o (Python) # after linked PARI by _Rémy Sigrist_

%o base, vv, nb = 10, [0], 0

%o def visit(v, s, z, r):

%o     global base, vv, nb

%o     if v and s==z:

%o         nb += 1

%o         if nb > len(vv): vv.append(len(vv))

%o         vv[nb-1] = v

%o     if s-z-r <= 0 and s-z+(base-1)*r >= 0:

%o         if v: visit(base*v, s, z+1, r-1)

%o         for d in range(1, base): visit(base*v+d, s+d, z, r-1)

%o def auptod(digits): visit(0, 0, 0, digits); return sorted(set(vv))

%o print(auptod(6)) # _Michael S. Branicky_, May 26 2022

%Y Subsequence of A011540.

%Y Cf. A007953 (sum of digits), A055641 (number of 0's).

%Y Cf. A031443, A061384.

%K nonn,base

%O 1,1

%A _Tamas Sandor Nagy_, May 25 2022