A256222 Largest Fibonacci number in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3, ..., 1/n.

0, 1, 3, 5, 13, 13, 13, 89, 89, 89, 1597, 1597, 1597, 1597, 1597, 1597, 17711, 17711, 17711, 28657, 28657, 28657, 28657, 1346269, 1346269, 1346269, 1346269, 24157817, 24157817, 24157817, 24157817, 24157817, 24157817, 39088169, 39088169, 39088169, 39088169

Offset: 0

Author

Michel Lagneau, Mar 19 2015

Keywords

• nonn

Comments

The prime Fibonacci numbers in the sequence are 3, 5, 13, 89, 1597, 28657, ...

For information about how often the numerator of these sums is a Fibonacci number, see A256220 and A256221.

Examples

			a(3) = 5 because we obtain the 5 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 => the greatest Fibonacci number is 5.
		

Links

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

Crossrefs

Cf. A000045, A005478, A075226, A256220, A256221, A256223.

Programs

Mathematica

<<"DiscreteMath`Combinatorica`"; maxN=24; For[t={}; mx=0; i=0; n=0, 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]], If[k>mx, t=s]; mx=Max[mx, k]]]; Print[mx]]

Extensions

Corrected and extended by Alois P. Heinz, Mar 25 2015

a(30)-a(36) from Hiroaki Yamanouchi, Mar 30 2015