A084176 - OEIS

%I #14 May 13 2013 01:54:07

%S 0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,18,21,22,23,24,26,29,34,35,36,

%T 37,39,42,47,55,56,57,58,60,63,68,76,89,90,91,92,94,97,102,110,123,

%U 144,145,146,147,149,152,157,165,178,199,233,234,235,236,238,241,246

%N Sums of two Fibonacci numbers (allowing 0 as a summand).

%H Charles R Greathouse IV, <a href="/A084176/b084176.txt">Table of n, a(n) for n = 1..10000</a>

%F log a(n) ~ sqrt(n log phi) where phi is the golden ratio A001622. There are (log x/log phi)^2 + O(log x) members of this sequence up to x. - _Charles R Greathouse IV_, Jul 24 2012

%e 14=13+1, so is in, however 17 is not expressible as Fib(i)+Fib(j).

%o (PARI) list(lim)=my(upper=log(lim*sqrt(5))\log((1+sqrt(5))/2)+1, t, tt, v=List([0,1,2])); if(fibonacci(t)>lim,t--); for(i=3,upper, t=fibonacci(i); for(j=2,i-1,tt=t+fibonacci(j); if(tt>lim, break, listput(v,tt)))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 24 2012

%Y Cf. A000045. Essentially the same as A059389.

%K nonn,easy

%O 1,3

%A _Jon Perry_, Jun 20 2003