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%I #11 Jun 06 2016 02:12:34
%S 1,4,1,7,7,4,2,5,4,6,1,8,1,3,8,8,3,1,4,2,8,8,2,9,0,9,1,0,9,9,0,0,0,6,
%T 6,2,9,5,3,1,7,9,5,3,2,0,5,7,7,1,7,7,2,5,6,8,8,0,9,1,2,2,1,2,9,6,1,2,
%U 9,9,3,2,0,3,7,6,0,5,6,5,0,4,3,5,4,6,6,9,0,8,0,7,3,2,3,3,7,3,8,3,6,2,1,1,1
%N Decimal expansion of constant C>0 such that sum(k>=1,1/C^(k^2)) = 1.
%e 1.417742546...
%t c /. FindRoot[ EllipticTheta[3, 0, 1/c] == 3, {c, 3/2}, WorkingPrecision -> 110] // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 15 2013 *)
%o (PARI) th3(x)=1 + 2*suminf(n=1,x^n^2)
%o solve(x=1.4,2,th3(1/x)-3) \\ _Charles R Greathouse IV_, Jun 06 2016
%K cons,nonn
%O 1,2
%A _Benoit Cloitre_, Jan 12 2003