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A290748 Let F denote the two-way infinite sequence of Fibonacci numbers (for all positive or negative integers k, F(k+2)=F(k)+F(k+1) with F(0)=0, F(1)=1). Sequence lists positive numbers that are the difference between two terms of F.

%I A290748 #29 Dec 23 2024 14:53:45
%S A290748 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18,19,20,21,22,23,24,26,29,31,32,
%T A290748 33,34,35,37,42,47,50,52,53,54,55,56,57,58,60,63,68,76,81,84,86,87,88,
%U A290748 89,90,92,97,110,123,131,136,139,141,142,143,144,145,146
%N A290748 Let F denote the two-way infinite sequence of Fibonacci numbers (for all positive or negative integers k, F(k+2)=F(k)+F(k+1) with F(0)=0, F(1)=1). Sequence lists positive numbers that are the difference between two terms of F.
%H A290748 Robert Israel, <a href="/A290748/b290748.txt">Table of n, a(n) for n = 1..10000</a>
%H A290748 Don Reble, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2017-August/017856.html">Difference of Fibonacci's</a>, Posting to Sequence Fans Mailing List, Aug 10 2017.
%e A290748 9 is here because F(6) - F(-2) = 8 - (-1) = 9.
%p A290748 N:= 40: # to get all terms <= F(N) - F(N-1)
%p A290748 P:= sort(convert({seq(combinat:-fibonacci(n),n=-N..N)},list)):
%p A290748 sort(convert(select(`<=`,{seq(seq(P[i]-P[j],j=1..i-1),i=1..nops(P))},P[-1]-P[-2]),list)): # _Robert Israel_, Aug 11 2017
%t A290748 Select[Union[Subtract @@@ Tuples[Fibonacci[Range[-30, 30]], 2]], 0 < # < 150 &] (* _Giovanni Resta_, Aug 11 2017 *)
%Y A290748 Cf. A000045, A007298 (if we only use F(k) for k >= 0).
%Y A290748 See A290749 for the complement.
%K A290748 nonn
%O A290748 1,2
%A A290748 _N. J. A. Sloane_, Aug 11 2017
%E A290748 Corrected by _R. J. Mathar_, Aug 10 2017
%E A290748 More terms from _Giovanni Resta_, Aug 11 2017