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%I #14 Nov 09 2020 09:06:02
%S 1,1,2,3,5,13,377,10946
%N a(1) = 1, a(2) = 1, a(n+1) = least Fibonacci number of the form k*(a(n-1)) - a(n), not included earlier.
%C No further terms exist since there is no Fibonacci number congruent to -10946 modulo 377. - _Max Alekseyev_, Jun 16 2011
%e 377 = 5*78 -13, k = 78.
%t a[1] = a[2] = 1;
%t a[n_] := a[n] = For[i = 1, True, i++, f = Fibonacci[i]; If[FreeQ[Array[a, n-1], f] && IntegerQ[(f + a[n-1])/a[n-2]], Return[f]]];
%t Array[a, 8] (* _Jean-François Alcover_, Nov 09 2020 *)
%Y Cf. A114748.
%K nonn,fini,full
%O 1,3
%A _Amarnath Murthy_, Nov 15 2005
%E Keywords fini, full from _Max Alekseyev_, Jun 16 2011