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1, 19, 199, 1999, 19999, 199999, 1999999, 19999999, 199999999, 1999999999, 19999999999, 199999999999, 1999999999999, 19999999999999, 199999999999999, 1999999999999999, 19999999999999999, 199999999999999999, 1999999999999999999
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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 (amarnath_murthy(AT)yahoo.com), 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
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
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FORMULA
| a(n)=2*10^(n-1)-1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 28 2002
a(n) = 10*a(n-1)+9. - Vincenzo Librandi, Nov 01 2011
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EXAMPLE
| T(19) = 190 begins with 19. Hence 19 is a term of the sequence.
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MATHEMATICA
| (*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} ]
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PROG
| (MAGMA) [2*10^(n-1)-1 : n in [1..20]]; // Vincenzo Librandi, Nov 01 2011
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CROSSREFS
| Sequence in context: A147830 A135162 A185687 * A037071 A065582 A055558
Adjacent sequences: A067269 A067270 A067271 * A067273 A067274 A067275
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KEYWORD
| nonn,easy
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 21 2002
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EXTENSIONS
| a(7)-a(19) from Vincenzo Librandi, Nov 01 2011
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