login
a(n) is the greatest Fibonacci number < 2^(n+1).
2

%I #9 Jan 09 2021 07:37:13

%S 1,3,5,13,21,55,89,233,377,987,1597,2584,6765,10946,28657,46368,

%T 121393,196418,514229,832040,1346269,3524578,5702887,14930352,

%U 24157817,63245986,102334155,267914296,433494437,701408733,1836311903,2971215073,7778742049,12586269025

%N a(n) is the greatest Fibonacci number < 2^(n+1).

%C a(n) is also the greatest Fibonacci number whose binary expansion has n+1 digits.

%F 2^n <= A340399(n) <= a(n) < 2^(n+1).

%o (PARI) a(n) = my (g=0); for (i=1, oo, my (f=fibonacci(i)); if (f>=2^(n+1), return (g), g=f))

%Y Cf. A000045, A000079, A340399.

%K nonn

%O 0,2

%A _Rémy Sigrist_, Jan 06 2021