A199552 4*8^n+1.

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

Offset: 0

Author

Vincenzo Librandi, Nov 08 2011

Keywords

• nonn
• easy

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).

Crossrefs

A087289, A199493.

Programs

Magma

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

Mathematica

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

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)).