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A083683 a(n) = 11*2^n + 1. 10
12, 23, 45, 89, 177, 353, 705, 1409, 2817, 5633, 11265, 22529, 45057, 90113, 180225, 360449, 720897, 1441793, 2883585, 5767169, 11534337, 23068673, 46137345, 92274689, 184549377, 369098753, 738197505, 1476395009, 2952790017, 5905580033, 11811160065 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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An Engel expansion of 2/11 to the base 2 as defined in A181565, with the associated series expansion 2/11 = 2/12 + 2^2/(12*23) + 2^3/(12*23*45) + 2^4/(12*23*45*89) + .... - Peter Bala, Oct 29 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

C. P. Simoes, Teste de Desempenho Mental.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

a(n) = 2*a(n-1) - 1.

a(n) = 3*a(n-1) - 2*a(n-2), n>1. - Vincenzo Librandi, Nov 03 2011

G.f. (12-13*x)/((2*x-1)*(x-1)). - R. J. Mathar, Nov 03 2011

MATHEMATICA

s=12; lst={s}; Do[s=s+(s-1); AppendTo[lst, s], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 30 2009 *)

11*2^Range[0, 30]+1 (* or *) LinearRecurrence[{3, -2}, {12, 23}, 40] (* Harvey P. Dale, Aug 17 2017 *)

PROG

(MAGMA) [11*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011

(PARI) a(n)=11*2^n+1 \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Cf. A020737, A083575, A083686, A083705, A168596, A181565, A195744.

Sequence in context: A255729 A190426 A207539 * A294139 A255766 A015447

Adjacent sequences:  A083680 A083681 A083682 * A083684 A083685 A083686

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 15 2003

STATUS

approved

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Last modified February 20 20:55 EST 2019. Contains 320345 sequences. (Running on oeis4.)