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%I #12 Jan 06 2019 04:54:45
%S 4,3,11,131,17291,298995971,89398590973228811,
%T 7992108067998667938125889533702531,
%U 63873791370569400659097694858350356285036046451665934814399129508491
%N a(1) = 4; a(2) = 3; for n > 2, a(n) = a(n-1)^2 + a(n-1) - 1.
%C a(n) = -1 + Product_{k=1..n-1} a(k) for n > 1.
%C Sequence is a variant of A005267 (start values 3 and 2, offset 0). Both sequences have the same recursion formulas and both are infinite coprime sequences; a(n) has digital root 2 for odd n and 5 for even n, n > 2.
%C a(2) to a(6) are prime, a(1) and a(7) to a(10) are composite, a(2) to a(10) are squarefree.
%e a(3) = 3^2 + 3 - 1 = 11, a(4) = 11^2 + 11 - 1 = 131.
%p a[1]:=1: a[2]:=3: for n from 3 to 10 do a[n]:=a[n-1]^2+a[n-1]-1 od: seq(a[n],n=1..10); # _Emeric Deutsch_, Jan 09 2007
%t Join[{4},NestList[#^2+#-1&,3,10]] (* _Harvey P. Dale_, Jul 24 2012 *)
%o (PARI) 1. {print1(4,",",a=3,",");for(n=1,8,print1(a=a^2+a-1,","))}
%o 2. {m=10;v=vector(m);print1(v[1]=4,",");for(n=2,m,print1(v[n]=-1+prod(k=1,n-1,v[k]),","))} \\ _Klaus Brockhaus_, Jan 09 2007
%Y Cf. A005267.
%K nonn
%O 1,1
%A _Tomas Xordan_, Jan 06 2007
%E Edited and extended by _Klaus Brockhaus_ and _Emeric Deutsch_, Jan 09 2007
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