Search: id:A135927
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%I A135927
%S A135927 10,98,9602,92198402,8500545331353602,72259270930397519221389558374402,
%T A135927 5221402235392591963136699520829303150191924374488750728808857602
%N A135927 a(n) = a(n-1)^2 - 2 with a1=10.
%C A135927 This is the Lucas-Lehmer sequence with starting value u1=10 and the position 
               of the zeros when it is reduced mod(2^p-1) also gives the position 
               of the Mersenne primes. As we have started with n=1, these will occupy 
               the (p-1)th positions in the sequence. For example, the first 12 
               terms mod(2^13-1) are 10, 98, 1411, 506, 2113, 672, 1077, 4996, 2037, 
               4721, 128, 0 and hence 8191 is a Mersenne prime. The radicals in 
               the above closed forms are the solutions to x^2-10x+1=0.
%D A135927 Robinson, Raphael M.; Mersenne and Fermat Numbers, Proceedings of the 
               American Mathematical Society, Vol. 5, No. 5. (October 1954), pp. 
               842-846.
%F A135927 a(n)=2 cosh[2^(n-1) Log(5+2Sqrt(6))]=Exp[2^(n-1) Log(5+2Sqrt(6))]+ Exp[2^(n-1) 
               Log(5-2Sqrt(6))]= (5+2Sqrt(6))^(2^(n-1))+ (5-2Sqrt(6))^(2^(n-1))=Ceiling[Exp[2^(n-1) 
               Log(5+2Sqrt(6))]]=Ceiling[(5+2Sqrt(6))^(2^(n-1))].
%e A135927 2Cosh[2^3 Log[(5+2Sqrt(6))]=92198402, so a(4)=92198402
%t A135927 a[1]=10;a[n_]:=a[n]=a[n-1]^2-2;a[ # ]&/@Range[7]
%Y A135927 Cf. A000668, A000043, A003010, A095847, A001566, A135928.
%Y A135927 Sequence in context: A125445 A163446 A007137 this_sequence A129542 A081109 
               A004189
%Y A135927 Adjacent sequences: A135924 A135925 A135926 this_sequence A135928 A135929 
               A135930
%K A135927 easy,nonn
%O A135927 1,1
%A A135927 Ant King (mathstutoring(AT)ntlworld.com), Dec 07 2007

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