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

10, 200, 1001, 1010, 1100, 3000, 10002, 10020, 10200, 12000, 20001, 20010, 20100, 21000, 40000, 100003, 100011, 100030, 100101, 100110, 100300, 101001, 101010, 101100, 103000, 110001, 110010, 110100, 111000, 130000, 200002, 200020, 200200, 202000, 220000

Offset: 1

Author

Tamas Sandor Nagy, May 25 2022

Keywords

• nonn
• base

Comments

As is normal, there are no leading zeros. The places of k zeros and the nonzero digits that are partitions of k are combinatorial.

Numbers k such that A007953(k) = A055641(k). - Felix Fröhlich, May 26 2022

Links

• Rémy Sigrist, PARI program

Crossrefs

Subsequence of A011540.

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

Cf. A031443, A061384.

Programs

Mathematica

Select[Range[250000],DigitCount[#,10,0]==Total[IntegerDigits[#]]&] (* Harvey P. Dale, Jan 12 2023 *)

PARI

isok(m) = my(d=digits(m)); vecsum(d) == #select(x->(x==0), d); \\ Michel Marcus, May 26 2022

PARI

See Links section.

Python

# after linked PARI by Rémy Sigrist
base, vv, nb = 10, [0], 0
def visit(v, s, z, r):
    global base, vv, nb
    if v and s==z:
        nb += 1
        if nb > len(vv): vv.append(len(vv))
        vv[nb-1] = v
    if s-z-r <= 0 and s-z+(base-1)*r >= 0:
        if v: visit(base*v, s, z+1, r-1)
        for d in range(1, base): visit(base*v+d, s+d, z, r-1)
def auptod(digits): visit(0, 0, 0, digits); return sorted(set(vv))
print(auptod(6)) # Michael S. Branicky, May 26 2022