A228778 a(n) = 2^Fibonacci(n) + 1.

2, 3, 3, 5, 9, 33, 257, 8193, 2097153, 17179869185, 36028797018963969, 618970019642690137449562113, 22300745198530623141535718272648361505980417, 13803492693581127574869511724554050904902217944340773110325048447598593

Offset: 0

Author

Yeshwant Shivrai Valaulikar and M. Tamba, Sep 04 2013

Keywords

• nonn

Crossrefs

Cf. A000045, A000301, A063896.

Programs

Maple

a:= n-> 1 + 2^(<<0|1>, <1|1>>^n)[1,2]:
seq(a(n), n=0..15);  # Alois P. Heinz, Aug 12 2017

Mathematica

Table[2^Fibonacci[n] + 1, {n, 0, 13}] (* T. D. Noe, Sep 07 2013 *)

Formula

a(n+2) = a(n+1)*a(n) - a(n) - a(n+1) + 2, a(0)=2, a(1)=3.

Binet type formula: log_2(a(n)-1) = (1/sqrt(5)) * (r^n - s^n), where r and s are the roots of x^2-x-1. (this is true by definition).

a(n) = A000301(n) + 1 = A063896(n) + 2. - Alois P. Heinz, Aug 12 2017