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A067272 2*10^(n-1)-1. 5
1, 19, 199, 1999, 19999, 199999, 1999999, 19999999, 199999999, 1999999999, 19999999999, 199999999999, 1999999999999, 19999999999999, 199999999999999, 1999999999999999, 19999999999999999, 199999999999999999, 1999999999999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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, 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.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

a(n) = 2*10^(n-1)-1 - Benoit Cloitre, Feb 28 2002

a(n) = 10*a(n-1)+9. - Vincenzo Librandi, Nov 01 2011

G.f.: x*(1+8*x)/((1-x)*(1-10*x)). - Vincenzo Librandi, Aug 13 2014

EXAMPLE

T(19) = 190 begins with 19. Hence 19 is a term of the sequence.

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} ]

CoefficientList[Series[(1 + 8 x)/((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 13 2014 *)

PROG

(MAGMA) [2*10^(n-1)-1 : n in [1..20]]; // Vincenzo Librandi, Nov 01 2011

CROSSREFS

Sequence in context: A147830 A135162 A185687 * A065582 A241021 A055558

Adjacent sequences:  A067269 A067270 A067271 * A067273 A067274 A067275

KEYWORD

nonn,easy

AUTHOR

Joseph L. Pe, Feb 21 2002

EXTENSIONS

a(7)-a(19) from Vincenzo Librandi, Nov 01 2011

STATUS

approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)