A199552 a(n) = 4*8^n + 1.

5, 33, 257, 2049, 16385, 131073, 1048577, 8388609, 67108865, 536870913, 4294967297, 34359738369, 274877906945, 2199023255553, 17592186044417, 140737488355329, 1125899906842625, 9007199254740993, 72057594037927937, 576460752303423489, 4611686018427387905, 36893488147419103233

Offset

0,1

Comments

An Engel expansion of 2 to the base 8 as defined in A181565, with the associated series expansion 2 = 8/5 + 8^2/(5*33) + 8^3/(5*33*257) + 8^4/(5*33*257*2049) + .... Cf. A087289 and A199493. - 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 (9,-8).

Formula

a(n) = 8*a(n-1) - 7.

a(n) = 9*a(n-1) - 8*a(n-2).

G.f.: (5-12*x)/((1-x)*(1-8*x)).

From Elmo R. Oliveira, Sep 19 2025: (Start)

E.g.f.: exp(x)*(1 + 4*exp(7*x)).

a(n) = A013731(n) + 1. (End)

Mathematica

4*8^Range[0, 20]+1 (* Harvey P. Dale, Mar 18 2018 *)
(* Alternative: *)
LinearRecurrence[{9, -8}, {5, 33}, 20] (* Harvey P. Dale, Mar 18 2018 *)

Prog

(Magma) [4*8^n+1: n in [0..30]];

Crossrefs

Cf. A013731, A087289, A199493.

Sequence in context: A324312 A225612 A330802 * A361411 A395060 A061253

Adjacent sequences: A199549 A199550 A199551 * A199553 A199554 A199555

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Nov 08 2011

Status

approved