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A354410 Numbers with as many zeros as the sum of their digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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).
Sequence in context: A001085 A079436 A285021 * A126431 A335649 A202436
KEYWORD
nonn,base
AUTHOR
Tamas Sandor Nagy, May 25 2022
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)