%I A105394
%S A105394 1,2,0,7,2,9,1,9,9,6,9,8,5,7,4,7,0,7,4,4,1,7,2,0,4,1,8,4,2,5,7,6,9,9,9,
%T A105394 4,5,3,0,6,9,2,1,4,5,4,0,1,9,0,3,6,3,7,6,9,5,1,3,1,1,5,9,4,2,2,1,2,2,4,
%U A105394 0,0,1,5,4,0,7,0,3,5,7,7,6,1,6,7,7,6,5,5,9,7,8,6,8,8,9,9,9,2
%N A105394 Decimal expansion of sum of reciprocals of squares of Lucas numbers.
%C A105394 This is one of a set of related number theory constants. It is conjectured 
               to be irrational. T. D. Noe (noe(AT)sspectra.com) extended the digits 
               of this constant to 100 digits accuracy, when J. V. Post had discovered 
               it and found it to 8 digits. The reciprocal Fibonacci constant sum 
               1/F(n) ~ 3.35988566 is given in A079586, queried as to irrationality 
               by Erdos and proved irrational by Andre-Jeannin (1989). The reciprocal 
               Lucas constant sum 1/L(n) ~ 1.96285817 is given in A093540. Sum 1/
               L(n)^2 converges because each term is equal or less than the corresponding 
               term in the converging reciprocal Lucas constant. The sum 1/F(n)^2 
               is given in A105393.
%D A105394 R. Andre-Jeannin, "Irrationalite de la somme des inverses de certaines 
               suites recurrentes." C. R. Acad. Sci. Paris Ser. I Math. 308, 539-541, 
               1989.
%H A105394 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LucasNumber.html">Lucas Number.</a>
%H A105394 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FibonacciNumber.html">Fibonacci Number.</a>
%H A105394 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ReciprocalFibonacciConstant.html">Reciprocal Fibonacci Constant.</
               a>
%F A105394 Decimal expansion of Sum 1/L(n)^2.
%e A105394 1.207291996985747074417204
%Y A105394 Cf. A079586, A093540, A105393.
%Y A105394 Sequence in context: A022897 A156442 A140663 this_sequence A011343 A021486 
               A104540
%Y A105394 Adjacent sequences: A105391 A105392 A105393 this_sequence A105395 A105396 
               A105397
%K A105394 cons,easy,nonn
%O A105394 1,2
%A A105394 Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 04 2005