A166118 Fixed points of the mapping f(x) = (x + 2^x) mod (17 + x).

15, 47, 111, 239, 495, 1007, 2031, 4079, 8175, 16367, 32751, 65519, 131055, 262127, 524271, 1048559, 2097135, 4194287, 8388591, 16777199, 33554415, 67108847, 134217711, 268435439, 536870895, 1073741807, 2147483631, 4294967279

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 2*a(n-1) + 17, a(1) = 15.

a(n) = 16*2^n - 17.

From Colin Barker, Jan 25 2012: (Start)

a(n) = 3*a(n-1) - 2*a(n-2), a(1)=15, a(2)=47.

G.f.: x*(15+2*x)/(1-3*x+2*x^2). (End)

E.g.f.: 16*exp(2*x) - 17*exp(x) + 1. - G. C. Greubel, Apr 26 2016

Mathematica

(*1*) fp[n_]:=FixedPoint[Mod[(#+2^#), 17+# ]&, n] NestList[fp[2#+17]&, 15, 10]
(*2*)NestList[2*#+17&, 15, 40]
LinearRecurrence[{3, -2}, {15, 47}, 10] (* G. C. Greubel, Apr 26 2016 *)

Prog

(PARI) a(n)=([0, 1; -2, 3]^n*[-1; 15])[1, 1] \\ Charles R Greathouse IV, Apr 29 2016

Crossrefs

Cf. A166112.

Sequence in context: A105572 A143031 A214675 * A063396 A236401 A000813

Adjacent sequences: A166115 A166116 A166117 * A166119 A166120 A166121

Keyword

nonn,easy

Author

Zak Seidov, Oct 07 2009

Status

approved