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A256222 Largest Fibonacci number in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3, ..., 1/n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

LINKS

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

EXAMPLE

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.

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]]

CROSSREFS

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

Sequence in context: A231897 A260416 A328380 * A258976 A137162 A293863

Adjacent sequences:  A256219 A256220 A256221 * A256223 A256224 A256225

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 19 2015

EXTENSIONS

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

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

STATUS

approved

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Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)