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 A215422 Length of binary representation of Fibonacci(2^n). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n+1)/a(n)->2 as n->infinity. LINKS 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. A020909, 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

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Last modified March 24 18:34 EDT 2023. Contains 361510 sequences. (Running on oeis4.)