Search: id:A085579
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%I A085579
%S A085579 9,3,1,4,8,4,2,8,6,7,0,8,0,4,4,3,8,1,7,6,8,6,4,9,9,5,3,6,3,6,1,3,7,9,3,
%T A085579 4,1,7,1,0,8,0,2,2,1,8,2,8,3,7,2,3,1,0,2,4,4,4,6,6,6,7,2,5,9,0,2,3,2,5,
%U A085579 2,2,7,1,6,8,7,3,3,0,8,8,0,8,1,9,1,6,5,4,2,8,3,5,4,3,9,8,0,5
%N A085579 See comments lines for definition.
%C A085579 K = 2 in the script below. Conjecture: this diagonal expressed as a decimal 
               is irrational and transcendental. Proof? Counterexample?
%C A085579 Write down the floating point constants x(m)>0 which solve x^2+mx=2, 
               one per row for m=1,2,3,...:
%C A085579 0.99999999999999999999...
%C A085579 0.73205080756887729353...
%C A085579 0.56155281280883027491...
%C A085579 0.44948974278317809820...
%C A085579 0.37228132326901432993...
%C A085579 0.31662479035539984911...
%C A085579 and read this diagonally, the first digit after the dot from the first 
               constant, the 2nd digit after the dot from the 2nd constant, the 
               3rd digit after the dot from the 3rd constant etc.
%F A085579 Also the decimal expansion of the positive solutions x of the quadratic 
               equation x^2 + mx - 2 = 0, m = 1, 2... x = (sqrt(m^2+8)-2)/2 m=1, 
               2..
%o A085579 (PARI) diagonal(n,k) = { default(realprecision,n); for(m=1,n, s=.1; for(x=1,
               n, s=k/(s+m); ); a = Vec(Str(s)); print1(eval(a[m+2])","); ) }
%Y A085579 Sequence in context: A093312 A154629 A154489 this_sequence A081813 A048799 
               A086232
%Y A085579 Adjacent sequences: A085576 A085577 A085578 this_sequence A085580 A085581 
               A085582
%K A085579 easy,base,nonn
%O A085579 1,1
%A A085579 Cino Hilliard (hillcino368(AT)gmail.com), Jul 06 2003
%E A085579 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 01 2008

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