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

1,1

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

Table of n, a(n) for n=1..35.

Rémy Sigrist, PARI program

Mathematica

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

Prog

(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

Crossrefs

Subsequence of A011540.

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

Cf. A031443, A061384.

Sequence in context: A001085 A079436 A285021 * A126431 A335649 A202436

Adjacent sequences: A354407 A354408 A354409 * A354411 A354412 A354413

Keyword

nonn,base

Author

Tamas Sandor Nagy, May 25 2022

Status

approved