A057146 The sequence 2, floor(a), floor(a^2), floor(a^3), ..., with a = 1+sqrt(5).

2, 3, 10, 33, 109, 354, 1148, 3716, 12026, 38918, 125943, 407562, 1318899, 4268047, 13811692, 44695576, 144637922, 468058148, 1514667986, 4901568568, 15861809082, 51329892437, 166107021206, 537533612162, 1739495309150, 5629125066952, 18216231370504

Offset: 0

Author

N. J. A. Sloane, Sep 12 2000, May 14 2007

Keywords

• nonn

Links

• G. Harman, One hundred years of normal numbers

Crossrefs

Cf. A014217.

Programs

Magma

[2] cat [Floor((1+Sqrt(5))^n): n in [1..30]]; // Vincenzo Librandi, Feb 20 2016

Mathematica

Join[{2}, Table[Floor[(Sqrt[5] + 1)^n], {n, 1, 30}]] (* Artur Jasinski, Nov 22 2006 *)

PARI

a(n) = if (n==0, 2, floor((1+sqrt(5))^n)); \\ Michel Marcus, Feb 19 2016

Formula

a(n) = floor( (1+sqrt(5))^n ) for n>0, a(0)=2. - Artur Jasinski, Nov 22 2006