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A067272
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a(n) = 2*10^(n-1)-1.
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7
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1, 19, 199, 1999, 19999, 199999, 1999999, 19999999, 199999999, 1999999999, 19999999999, 199999999999, 1999999999999, 19999999999999, 199999999999999, 1999999999999999, 19999999999999999, 199999999999999999, 1999999999999999999
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Smaller of the smallest pair of successive n-digit numbers which have no digit in common: (1, 2), (19, 20), 199, 200) etc. - Amarnath Murthy, Nov 10 2002
Original name: Numbers n such that the digits of T(n) = n(n+1)/2, the n-th triangular number, begin with n.
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LINKS
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FORMULA
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EXAMPLE
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T(19) = 190 begins with 19. Hence 19 is a term of the sequence.
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MATHEMATICA
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(*returns true if a begins with b, false o.w.*) f2[a_, b_] := Module[{c, d, e, g, h, i, r}, r = False; c = ToString[a]; d = ToString[b]; g = StringPosition[c, d]; h = Length[g]; If[h > 0, i = g[[h]]; If[i[[1]] == 1, r = True]]; r]; Do[If[f2[n(n + 1)/2, n], Print[n]], {n, 1, 10^6} ]
CoefficientList[Series[(1 + 8 x)/((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 13 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,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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