A190407 - OEIS

%I #23 Mar 16 2020 09:29:25

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

%C See A190404.

%H Danny Rorabaugh, <a href="/A190407/b190407.txt">Table of n, a(n) for n = 0..10000</a>

%F Equals Sum_{k>=1} (1/2)^V(k), where V=A058331 (1+2*k^2).

%e 0.12695503246504857842...

%t (* See also A190404 *)

%t RealDigits[(EllipticTheta[3, 0, 1/4]-1)/4, 10, 120] // First (* _Jean-François Alcover_, Feb 13 2013 *)

%o (Sage)

%o def A190407(b): # Generate the constant with b bits of precision

%o     return N(sum([(1/2)^(2*k^2+1) for k in range(1,b)]),b)

%o A190407(415) # _Danny Rorabaugh_, Mar 26 2015

%o (PARI) th3(x)=1 + 2*suminf(n=1,x^n^2)

%o (th3(1/4)-1)/4 \\ _Charles R Greathouse IV_, Jun 06 2016

%Y Cf. A058331, A190404, A190405, A190406.

%K nonn,cons,easy

%O 0,2

%A _Clark Kimberling_, May 10 2011