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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 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: A299440 A330401 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 added by Robert Israel, Dec 09 2016 STATUS approved

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Last modified September 25 06:05 EDT 2020. Contains 337335 sequences. (Running on oeis4.)