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.

1, 2, 2, 2, 2, 2, 21, 21, 21, 21, 34, 34, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 987, 987, 987, 987, 987, 987, 987, 987, 987, 987, 46368, 46368, 46368, 46368, 46368, 46368, 46368, 46368, 46368, 832040, 832040, 832040, 832040, 832040, 832040, 832040

Offset: 0

Author

Michel Lagneau, Mar 19 2015

Keywords

• nonn

Comments

The largest prime generated is given in A256222.

Examples

			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.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A000045, A075227, A256220, A256221, A256222.

Programs

Mathematica

<<"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]]]

Extensions

a(0) prepended and a(24)-a(47) added by Hiroaki Yamanouchi, Mar 30 2015