A084176 Sums of two Fibonacci numbers (allowing 0 as a summand).

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, 37, 39, 42, 47, 55, 56, 57, 58, 60, 63, 68, 76, 89, 90, 91, 92, 94, 97, 102, 110, 123, 144, 145, 146, 147, 149, 152, 157, 165, 178, 199, 233, 234, 235, 236, 238, 241, 246

Offset

1,3

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A000045. Essentially the same as A059389.

Sequence in context: A322547 A325202 A338973 * A059389 A191328 A064683

Adjacent sequences: A084173 A084174 A084175 * A084177 A084178 A084179

Keyword

nonn,easy

Author

Jon Perry, Jun 20 2003

Status

approved