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%I #13 Jan 01 2024 13:17:09
%S 2,3,8,34,89,987,196418,2178309,5702887,24157817,165580141,433494437,
%T 4807526976,12586269025,32951280099,86267571272,365435296162,
%U 956722026041,4052739537881,8944394323791464,23416728348467685
%N Fibonacci numbers that satisfy: Sum_{k>=1} 1/a(k) = 1, such that the partial sums are nearest to, but never exceed, unity.
%C Corresponding Fibonacci indices are given by A084907.
%H Amiram Eldar, <a href="/A084908/b084908.txt">Table of n, a(n) for n = 1..1332</a>
%F a(n) = A000045(A084907(n)+1). - _Amiram Eldar_, Nov 01 2019
%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, Fibonacci[m]]; s -= (1/Fibonacci[m]); While[Fibonacci[m] <= 1/s, m++], {21}]; 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(fibonacci(b),","))
%Y Cf. A000045, A084907, A084910.
%K nonn
%O 1,1
%A _Paul D. Hanna_, Jun 10 2003