%I
%S 2,3,5,8,10,15,26,31,33,36,40,42,47,49,51,53,56,58,61,77,79,81,84,88,
%T 90,92,95,97,99,102,104,106,111,113,115,120,122,127,129,132,136,138,
%U 141,145,147,150,157,159,162,164,172,177,181,183,185,200,203,206,209,211
%N Indices of Fibonacci numbers that satisfy: Sum_{k>=1} 1/F(a(k))) = 1, where F(k) gives the kth Fibonacci number with F(0)=1, such that the partial sums are nearest to, but never exceed, unity.
%C Corresponding Fibonacci numbers are given by A084908.
%H Amiram Eldar, <a href="/A084907/b084907.txt">Table of n, a(n) for n = 1..10000</a>
%e 1 = 1/F(2) + 1/F(3) + 1/F(5) + 1/F(8) + 1/F(10) + 1/F(15) + ... = 1/2 + 1/3 + 1/8 + 1/34 + 1/89 + 1/987 + 1/196418 + 1/2178309 +...
%t seq = {}; s = 1; m = 3; Do[AppendTo[seq, m  1]; s = (1/Fibonacci[m]); While[Fibonacci[m] <= 1/s, m++], {60}]; seq (* _Amiram Eldar_, Nov 01 2019 *)
%o (PARI) x=1; a=2; S=0; for(n=1,100,b=a+1; while(abs(S+1/fibonacci(b))>x,b++); S=S+1/fibonacci(b); a=b; print1(b1,","))
%Y Cf. A000045, A084908, A084909.
%K nonn
%O 1,1
%A _Paul D. Hanna_, Jun 10 2003
%E Terms a(41) onward corrected by _Amiram Eldar_, Nov 01 2019
