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A190407 Decimal expansion of Sum_{k>=1} (1/2)^A058331(k); based on a diagonal of the natural number array, A000027.

%I A190407 #23 Mar 16 2020 09:29:25
%S A190407 1,2,6,9,5,5,0,3,2,4,6,5,0,4,8,5,7,8,4,1,6,2,5,0,5,4,3,6,3,5,7,2,5,6,
%T A190407 7,8,8,0,6,9,6,2,1,6,8,1,9,0,1,4,6,8,0,0,2,3,1,5,0,6,1,7,8,4,9,2,5,0,
%U A190407 9,9,2,2,7,6,2,2,7,3,0,7,5,3,8,2,1,6,5,1,3,8,3,2,3,0,9,6,1,4,3,1,3,9,1,4,3,1,4,5,8,3,2,5,4,2,1,3,0,3,3,2
%N A190407 Decimal expansion of Sum_{k>=1} (1/2)^A058331(k); based on a diagonal of the natural number array, A000027.
%C A190407 See A190404.
%H A190407 Danny Rorabaugh, <a href="/A190407/b190407.txt">Table of n, a(n) for n = 0..10000</a>
%F A190407 Equals Sum_{k>=1} (1/2)^V(k), where V=A058331 (1+2*k^2).
%e A190407 0.12695503246504857842...
%t A190407 (* See also A190404 *)
%t A190407 RealDigits[(EllipticTheta[3, 0, 1/4]-1)/4, 10, 120] // First (* _Jean-François Alcover_, Feb 13 2013 *)
%o A190407 (Sage)
%o A190407 def A190407(b): # Generate the constant with b bits of precision
%o A190407     return N(sum([(1/2)^(2*k^2+1) for k in range(1,b)]),b)
%o A190407 A190407(415) # _Danny Rorabaugh_, Mar 26 2015
%o A190407 (PARI) th3(x)=1 + 2*suminf(n=1,x^n^2)
%o A190407 (th3(1/4)-1)/4 \\ _Charles R Greathouse IV_, Jun 06 2016
%Y A190407 Cf. A058331, A190404, A190405, A190406.
%K A190407 nonn,cons,easy
%O A190407 0,2
%A A190407 _Clark Kimberling_, May 10 2011