Search: id:A082732
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%I A082732
%S A082732 1,3,4,13,157,24493,599882557,359859081592975693,
%T A082732 129498558604939936868397356895854557,
%U A082732 16769876680757063368089314196389622249367851612542961252860614401811693
%N A082732 a(1) = 1, a(2) = 3, a(n) = LCM of all the previous terms + 1.
%C A082732 The LCM is in fact the product of all previous terms. From a(5) onwards 
               the terms alternately end in 57 and 93.
%F A082732 a(n+1) = a(n)^2 -a(n) + 1 for n >2.
%F A082732 1/3=1/4+1/13+1/157+1/24493+...1/a(n) n->Infinity or 1=3/4+3/13+3/157+3/
               24493+...3/a(n) n->Infinity [From Artur Jasinski (grafix(AT)csl.pl), 
               Sep 21 2008]
%F A082732 1/3=Sum[1/a[n+2],{n,1,Infinity}]=1/4+1/13+1/157+1/24493+...1/a(n) n->
               Infinity or 1=Sum[3/a[n+2],{n,1,Infinity}]=3/4+3/13+3/157+3/24493+...3/
               a(n) n->Infinity. If we take segment of length 1 and we will be cut 
               off in each step fragment maximal length such that numerator of fraction 
               is 3, denominators of such fractions will be successive numbers of 
               this sequence. [From Artur Jasinski (grafix(AT)csl.pl), Sep 22 2008]
%F A082732 a(n+2)=1.8806785436830780944921917650127503562630617563236301969047995953391\
%F A082732 4798717695395204087358090874194124503892563356447954254847544689332763...^(2^n) 
               [From Artur Jasinski (grafix(AT)csl.pl), Sep 22 2008]
%t A082732 a[1] = 1; a[2] = 3; a[n_] := Apply[LCM, Table[a[i], {i, 1, n - 1}]] + 
               1; Table[ a[n], {n, 1, 10}]
%t A082732 c=1.8806785436830780944921917650127503562630617563236301969047995953391479871\
%t A082732 7695395204087358090874194124503892563356447954254847544689332763; Table[c^(2^n),
               {n,1,6}] or a = {}; k = 4; Do[AppendTo[a, k]; k = k^2 - k + 1, {n, 
               1, 10}]; a [From Artur Jasinski (grafix(AT)csl.pl), Sep 22 2008]
%Y A082732 Cf. A000058.
%Y A082732 A000058, A082732, A144743, A144779, A144780, A144781, A144782, A144783, 
               A144784, A144785, A144786, A144787, A144788 [From Artur Jasinski 
               (grafix(AT)csl.pl), Sep 22 2008]
%Y A082732 Sequence in context: A062165 A001056 A122151 this_sequence A009286 A076663 
               A079274
%Y A082732 Adjacent sequences: A082729 A082730 A082731 this_sequence A082733 A082734 
               A082735
%K A082732 nonn
%O A082732 1,2
%A A082732 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 14 2003
%E A082732 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 15 2003

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