This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256223 #10 Mar 30 2015 13:49:34
%S A256223 1,2,2,2,2,2,21,21,21,21,34,34,144,144,144,144,144,144,144,144,144,
%T A256223 144,987,987,987,987,987,987,987,987,987,987,46368,46368,46368,46368,
%U A256223 46368,46368,46368,46368,46368,832040,832040,832040,832040,832040,832040,832040
%N A256223 Smallest Fibonacci number not occurring in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3,..., 1/n.
%C A256223 The largest prime generated is given in A256222.
%H A256223 Hiroaki Yamanouchi, <a href="/A256223/b256223.txt">Table of n, a(n) for n = 0..50</a>
%e A256223 a(3) = 2 because we obtain 5 following subsets {1}, {1/2}, {1/3}, {1, 1/2} and {1/2, 1/3} having 5 sums with Fibonacci numerators: 1, 1, 1, 1+1/2 = 3/2 and 1/2+1/3 = 5/6. Then, 2 is the smallest Fibonacci number not occurring in the numerator of the previous sums.
%t A256223 <<"DiscreteMath`Combinatorica`"; maxN=23; For[prms={}; i=0; n=1, n<=maxN, n++, While[i<2^n-1, i++; s=NthSubset[i, Range[n]]; k=Numerator[Plus@@(1/s)]; If[IntegerQ[Sqrt[5*k^2+4]]||IntegerQ[Sqrt[5*k^2-4]], AppendTo[prms, k]]]; prms=Union[prms]; j=2; While[MemberQ[prms, Fibonacci[j]], j++ ]; Print[Fibonacci[j]]]
%Y A256223 Cf. A000045, A075227, A256220, A256221, A256222.
%K A256223 nonn
%O A256223 0,2
%A A256223 _Michel Lagneau_, Mar 19 2015
%E A256223 a(0) prepended and a(24)-a(47) added by _Hiroaki Yamanouchi_, Mar 30 2015