A215422 Length of binary representation of Fibonacci(2^n).

1, 1, 2, 5, 10, 22, 44, 88, 177, 355, 710, 1421, 2843, 5687, 11374, 22748, 45497, 90995, 181991, 363982, 727965, 1455930, 2911861, 5823723, 11647446, 23294892, 46589786, 93179572, 186359144, 372718289

Offset

0,3

Comments

a(n+1)/a(n)->2 as n->infinity.

Links

Table of n, a(n) for n=0..29.

Formula

a(n) = A070939(A000045(A000079(n))).

a(n) = 2^n * log_2 phi + O(1). - Charles R Greathouse IV, Jun 05 2013

Mathematica

IntegerLength[Fibonacci[2^Range[0, 30]], 2] (* Harvey P. Dale, Apr 10 2019 *)

Prog

(Python)
TOP = 33
fib2m1 = [0]*TOP  # Fibonacci(2^n-1)
fib2   = [1]*TOP  # Fibonacci(2^n)
print(1, end=', ')
for n in range(1, TOP):
    fib2[n]   = (2*fib2m1[n-1] + fib2[n-1])*fib2[n-1]
    fib2m1[n] = fib2m1[n-1]*fib2m1[n-1] + fib2[n-1]*fib2[n-1]
    print(len(bin(fib2[n]))-2, end=', ')
(PARI) a(n) =  #binary(fibonacci(2^n)) \\ Michel Marcus, Jun 05 2013

Crossrefs

Cf. A000045, A000079, A020909, A070939, A215367.

Sequence in context: A002512 A097096 A073777 * A026633 A093370 A094537

Adjacent sequences: A215419 A215420 A215421 * A215423 A215424 A215425

Keyword

nonn,base

Author

Alex Ratushnyak, Aug 10 2012

Status

approved