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 A268099 a(n) = 2^(n mod 2)*5*10^floor(n/2) - 1. 0
 4, 9, 49, 99, 499, 999, 4999, 9999, 49999, 99999, 499999, 999999, 4999999, 9999999, 49999999, 99999999, 499999999, 999999999, 4999999999, 9999999999, 49999999999, 99999999999, 499999999999, 999999999999, 4999999999999, 9999999999999, 49999999999999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS These numbers x also have the property that the Fibonacci sequence starting (1, x, ...) contains the concatenation of 1 and x, but there are other solutions, e.g., x = 14285. LINKS R. Israel, in reply to E. Angelini, Fibonacci concatenated, SeqFan list, Jan. 26, 2016 Index entries for linear recurrences with constant coefficients, signature (1,10,-10). FORMULA G.f.: (-4/(1 - x) + (2*Sqrt(10))/(1 - Sqrt(10)*x) - 10/(-1 + Sqrt(10)*x) + 10/(1 + Sqrt(10)*x) - (2*Sqrt(10))/(1 + Sqrt(10)*x))/4. - Michael De Vlieger, Jan 26 2016 G.f.: ( 4+5*x ) / ( (x-1)*(10*x^2-1) ). - R. J. Mathar, Mar 12 2017 MATHEMATICA Table[2^Mod[n, 2]*5*10^Floor[n/2] - 1, {n, 0, 30}] (* or *) LinearRecurrence[{0, 10}, {5, 10}, 30] - 1 (* or *) CoefficientList[Series[(-4/(1 - x) + (2 Sqrt[10])/(1 - Sqrt[10] x) - 10/(-1 + Sqrt[10] x) + 10/(1 + Sqrt[10] x) - (2 Sqrt[10])/(1 + Sqrt[10] x))/4, {x, 0, 30}], x] (* Michael De Vlieger, Jan 26 2016 *) PROG (PARI) a(n)=2^bittest(n, 0)*5*10^(n\2)-1 CROSSREFS Sequence in context: A029791 A053961 A055812 * A061867 A019544 A053059 Adjacent sequences:  A268096 A268097 A268098 * A268100 A268101 A268102 KEYWORD nonn,easy AUTHOR M. F. Hasler, Jan 26 2016 STATUS approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)