cp's OEIS Frontend

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

%I A215422 #21 May 12 2023 15:33:30
%S A215422 1,1,2,5,10,22,44,88,177,355,710,1421,2843,5687,11374,22748,45497,
%T A215422 90995,181991,363982,727965,1455930,2911861,5823723,11647446,23294892,
%U A215422 46589786,93179572,186359144,372718289
%N A215422 Length of binary representation of Fibonacci(2^n).
%C A215422 a(n+1)/a(n)->2 as n->infinity.
%F A215422 a(n) = A070939(A000045(A000079(n))).
%F A215422 a(n) = 2^n * log_2 phi + O(1). - _Charles R Greathouse IV_, Jun 05 2013
%t A215422 IntegerLength[Fibonacci[2^Range[0,30]],2] (* _Harvey P. Dale_, Apr 10 2019 *)
%o A215422 (Python)
%o A215422 TOP = 33
%o A215422 fib2m1 = [0]*TOP  # Fibonacci(2^n-1)
%o A215422 fib2   = [1]*TOP  # Fibonacci(2^n)
%o A215422 print(1, end=',')
%o A215422 for n in range(1,TOP):
%o A215422     fib2[n]   = (2*fib2m1[n-1] + fib2[n-1])*fib2[n-1]
%o A215422     fib2m1[n] = fib2m1[n-1]*fib2m1[n-1] + fib2[n-1]*fib2[n-1]
%o A215422     print(len(bin(fib2[n]))-2, end=',')
%o A215422 (PARI) a(n) =  #binary(fibonacci(2^n)) \\ _Michel Marcus_, Jun 05 2013
%Y A215422 Cf. A000045, A000079, A020909, A070939, A215367.
%K A215422 nonn,base
%O A215422 0,3
%A A215422 _Alex Ratushnyak_, Aug 10 2012