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A048355
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a(n) is the index of the smallest triangular number containing exactly n 0's.
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11
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0, 24, 200, 775, 2000, 10000, 20000, 100000, 200000, 1000000, 2000000, 10000000, 20000000, 100000000, 200000000, 1000000000, 2000000000, 10000000000, 20000000000, 100000000000, 200000000000, 1000000000000, 2000000000000, 10000000000000, 20000000000000, 100000000000000
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OFFSET
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1,2
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LINKS
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FORMULA
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for n odd >= 5, a(n) = 2 * 10^((n+1)/2),
for n even >= 6, a(n) = 10^((n+2)/2).
(End)
G.f.: x^2*(24 + 200*x + 535*x^2 + 2250*x^4) / (1 - 10*x^2).
a(n) = 10*a(n-2) for n>4.
(End)
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EXAMPLE
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a(2) = 24: T(24) = 300 which contains exactly two 0's.
a(6) = 10000: T(10000) = 50005000 which contains exactly six 0's.
a(7) = 20000: T(20000) = 200010000 which contains exactly seven 0's.
(End)
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MATHEMATICA
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nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
n0 = Count[IntegerDigits[p], 0];
If[nsmall[[n0]] > i, nsmall[[n0]] = i]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)
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PROG
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(PARI) Vec(x^2*(24 + 200*x + 535*x^2 + 2250*x^4) / (1 - 10*x^2) + O(x^30)) \\ Colin Barker, Mar 25 2020
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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