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A083705 a(n) = 2*a(n-1) - 1 with a(0)=10. 10
10, 19, 37, 73, 145, 289, 577, 1153, 2305, 4609, 9217, 18433, 36865, 73729, 147457, 294913, 589825, 1179649, 2359297, 4718593, 9437185, 18874369, 37748737, 75497473, 150994945, 301989889, 603979777, 1207959553, 2415919105, 4831838209, 9663676417, 19327352833 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

An Engel expansion of 2/9 to the base 2 as defined in A181565, with the associated series expansion 2/9 = 2/10 + 2^2/(10*19) + 2^3/(10*19*37) + 2^4/(10*19*37*73) + .... - Peter Bala, Oct 29 2013

LINKS

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

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

FORMULA

From R. J. Mathar, Aug 01 2009: (Start)

a(n) = 1 + 9*2^n = 3*a(n-1) - 2*a(n-2).

G.f.: -(-10+11*x)/((2*x-1)*(x-1)). (End)

MATHEMATICA

s=10; lst={s}; Do[s=s+(s-1); AppendTo[lst, s], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 30 2009 *)

NestList[2#-1&, 10, 40]  (* Harvey P. Dale, Mar 13 2011 *)

PROG

(MAGMA) [9*2^n+1 : n in [0..30]]; // Vincenzo Librandi, Nov 03 2011

CROSSREFS

A020737, A083575, A083683, A083686, A168596, A181565, A195744.

Sequence in context: A085728 A195955 A127194 * A245003 A298487 A082659

Adjacent sequences:  A083702 A083703 A083704 * A083706 A083707 A083708

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 15 2003

STATUS

approved

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Last modified April 19 19:00 EDT 2019. Contains 322290 sequences. (Running on oeis4.)