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%I #2 Oct 19 2017 03:13:56
%S 1,2,4,3,10,12,7,20,6,8,11,5,21,16,9,35,13,72,58,65,604,1570,483,7868,
%T 43510,408,1092,659,2030,14316,8639,746852,19897158,2687632650,
%U 2999086659168,1284545911428706,223248740282126298936,327753663681964670057609684710,356988962448345124133946312923274915552122,585368332163743818626039069448750700022101290164211798116740578
%N a(n) is the smallest number not already used such that a(n)*a(n-1)*a(n-2) + 1 is a square, with a(1)=1 and a(2)=2.
%e a(3) = 4 because 1*2*4+1 = 9 = 3*3 a(4) = 3 because 2*4*3+1 = 25 = 5 * 5
%t a = {1, 2}; Do[ b = a[[ -2]]*a[[ -1]]; k = 3; While[ !IntegerQ[ Sqrt[k*b + 1]] || Position[a, k] != {}, k++ ]; Print[k]; a = Append[a, k], {n, 3, 33} ]; a
%K nonn,nice
%O 1,2
%A Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 11 2001
%E More terms from _Don Reble_, Oct 13 2001