A290748 - OEIS

%I #29 Dec 23 2024 14:53:45

%S 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 33,34,35,37,42,47,50,52,53,54,55,56,57,58,60,63,68,76,81,84,86,87,88,

%U 89,90,92,97,110,123,131,136,139,141,142,143,144,145,146

%N 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 Robert Israel, <a href="/A290748/b290748.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 9 is here because F(6) - F(-2) = 8 - (-1) = 9.

%p N:= 40: # to get all terms <= F(N) - F(N-1)

%p P:= sort(convert({seq(combinat:-fibonacci(n),n=-N..N)},list)):

%p 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 Select[Union[Subtract @@@ Tuples[Fibonacci[Range[-30, 30]], 2]], 0 < # < 150 &] (* _Giovanni Resta_, Aug 11 2017 *)

%Y Cf. A000045, A007298 (if we only use F(k) for k >= 0).

%Y See A290749 for the complement.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 11 2017

%E Corrected by _R. J. Mathar_, Aug 10 2017

%E More terms from _Giovanni Resta_, Aug 11 2017