Search: id:A065918
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%I A065918
%S A065918 1,3,1,6,9,5,7,8,9,6,9,2,4,8,1,6,7,0,8,6,2,5,0,4,6,3,4,7,3,0,7,9,6,8,4,
%T A065918 4,4,0,2,6,9,8,1,9,7,1,4,6,7,5,1,6,4,7,9,7,6,8,4,7,2,2,5,6,9,2,0,4,6,0,
%U A065918 1,8,5,4,1,6,4,4,3,9,7,6,0,7,4,2,1,9,0,1,3,4,5,0,1,0,1,7,8,3,5,5
%N A065918 ln(2+sqrt(3)).
%C A065918 x = 2^n -1 is prime if and only if x divides cosh( 2^(n-2) * ln(2+sqrt(3))).
%H A065918 Harry J. Smith, <a href="b065918.txt">Table of n, a(n) for n=1,...,2000</
               a>
%H A065918 Chris Caldwell, <a href="http://www.utm.edu/research/primes/prove/prove3_2.html">
               Primality Proving</a>, Arndt's theorem.
%e A065918 1.316957896924816708625046347307968444...
%o A065918 (PARI) { default(realprecision, 2080); x=log(2 + sqrt(3)); for (n=1, 
               2000, d=floor(x); x=(x-d)*10; write("b065918.txt", n, " ", d)) } 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 04 2009]
%Y A065918 Cf. A001075.
%Y A065918 Sequence in context: A013610 A008573 A089710 this_sequence A020861 A163213 
               A095066
%Y A065918 Adjacent sequences: A065915 A065916 A065917 this_sequence A065919 A065920 
               A065921
%K A065918 nonn,easy,cons,new
%O A065918 1,2
%A A065918 Frank.Ellermann(AT)t-online.de, Dec 08 2001

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