cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Alex Ratushnyak, Aug 10 2012

Keywords

Comments

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

Crossrefs

Programs

  • Mathematica
    IntegerLength[Fibonacci[2^Range[0,30]],2] (* Harvey P. Dale, Apr 10 2019 *)
  • PARI
    a(n) =  #binary(fibonacci(2^n)) \\ Michel Marcus, Jun 05 2013
  • 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=',')
    

Formula

a(n) = A070939(A000045(A000079(n))).
a(n) = 2^n * log_2 phi + O(1). - Charles R Greathouse IV, Jun 05 2013
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