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
Programs
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Mathematica
IntegerLength[Fibonacci[2^Range[0,30]],2] (* Harvey P. Dale, Apr 10 2019 *)
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PARI
a(n) = #binary(fibonacci(2^n)) \\ Michel Marcus, Jun 05 2013
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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) = 2^n * log_2 phi + O(1). - Charles R Greathouse IV, Jun 05 2013
Comments