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A215422
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Length of binary representation of Fibonacci(2^n).
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0
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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
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OFFSET
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0,3
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COMMENTS
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a(n+1)/a(n)->2 as n->infinity.
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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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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MATHEMATICA
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IntegerLength[Fibonacci[2^Range[0, 30]], 2] (* Harvey P. Dale, Apr 10 2019 *)
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PROG
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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=', ')
(PARI) a(n) = #binary(fibonacci(2^n)) \\ Michel Marcus, Jun 05 2013
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CROSSREFS
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Cf. A020909, A215367.
Sequence in context: A002512 A097096 A073777 * A026633 A093370 A094537
Adjacent sequences: A215419 A215420 A215421 * A215423 A215424 A215425
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KEYWORD
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nonn,base
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AUTHOR
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Alex Ratushnyak, Aug 10 2012
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STATUS
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approved
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