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A256221 Number of distinct nonzero Fibonacci numbers in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3, ..., 1/n. 3
1, 2, 3, 4, 5, 6, 8, 8, 8, 12, 12, 13, 13, 13, 13, 15, 15, 15, 17, 17, 17, 19, 21, 21, 23, 24, 25, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For the largest generated Fibonacci number, see A256222. For the smallest Fibonacci number not generated, see A256223.

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

a(4) = 4 because 4 sums yield distinct Fibonacci numerators: 1, 1+1/2 = 3/2, 1/2+1/3 = 5/6 and 1/2+1/3+1/4 = 13/12.

MAPLE

S:= {0, 1}: N:= {1}:

nfibs:= 10:

fibs:= {seq(combinat:-fibonacci(n), n=1..nfibs)}:

A[1]:= 1:

fibnums:= {1}:

for n from 2 to 24 do

    Sp:= map(`+`, S, 1/n);

    N:= N union map(numer, Sp);

  Nmax:= max(N);

  S:= S union Sp;

  while combinat:-fibonacci(nfibs) < Nmax do nfibs:= nfibs+1; fibs:= fibs union {combinat:-fibonacci(nfibs)} od;

  newfibnums:= N intersect fibs;

  fibnums:= newfibnums;

  A[n]:= nops(fibnums);

od:

seq(A[n], n=1..24); # Robert Israel, Dec 09 2016

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]], prms=Union[prms, {k}]]]; Print[Length[prms]]]

CROSSREFS

Cf. A000045, A075189, A010056, A256220, A256222, A256223.

Sequence in context: A274607 A262374 A145518 * A210253 A130916 A003965

Adjacent sequences:  A256218 A256219 A256220 * A256222 A256223 A256224

KEYWORD

nonn,more

AUTHOR

Michel Lagneau, Mar 19 2015

EXTENSIONS

Corrected and more terms by Robert Israel, Dec 09 2016

STATUS

approved

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Last modified March 27 12:31 EDT 2017. Contains 284176 sequences.