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A354410
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Numbers with as many zeros as the sum of their digits.
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1
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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)
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OFFSET
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1,1
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COMMENTS
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As is normal, there are no leading zeros. The places of k zeros and the nonzero digits that are partitions of k are combinatorial.
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LINKS
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MATHEMATICA
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Select[Range[250000], DigitCount[#, 10, 0]==Total[IntegerDigits[#]]&] (* Harvey P. Dale, Jan 12 2023 *)
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PROG
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(PARI) isok(m) = my(d=digits(m)); vecsum(d) == #select(x->(x==0), d); \\ Michel Marcus, May 26 2022
(PARI) See Links section.
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))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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