Search: id:A126604
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%I A126604
%S A126604 4,3,11,131,17291,298995971,89398590973228811,
%T A126604 7992108067998667938125889533702531,
%U A126604 63873791370569400659097694858350356285036046451665934814399129508491
%N A126604 a(1) = 4; a(2) = 3; for n>2, a(n) = a(n-1)^2 + a(n-1) - 1.
%C A126604 a(n) = -1 + Prod_{k=1..n-1}a(k) for n>1.
%C A126604 Sequence is a variant of A005267 (start values 3 and 2, offset 0). Both 
               sequences have the same recursion formulae and both are infinite 
               coprime sequences; a(n) has digital root 2 for odd n and 5 for even 
               n, n > 2.
%C A126604 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 A126604 a(3) = 3^2+3-1 = 11, a(4) = 11^2+11-1 = 131.
%p A126604 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 (deutsch(AT)duke.poly.edu), Jan 09 2007
%o A126604 (PARI) 1. {print1(4,",",a=3,",");for(n=1,8,print1(a=a^2+a-1,","))}
%o A126604 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 A126604 Cf. A005267.
%Y A126604 Sequence in context: A065337 A072802 A093726 this_sequence A099377 A121844 
               A091512
%Y A126604 Adjacent sequences: A126601 A126602 A126603 this_sequence A126605 A126606 
               A126607
%K A126604 nonn
%O A126604 1,1
%A A126604 Tomas Xordan (xordan.tom(AT)gmail.com), Jan 06 2007
%E A126604 Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) 
               and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 09 2007

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