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

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, 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, 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

Offset

0,2

Comments

See A190404.

Links

Danny Rorabaugh, Table of n, a(n) for n = 0..10000

Formula

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

Example

0.12695503246504857842...

Mathematica

(* See also A190404 *)
RealDigits[(EllipticTheta[3, 0, 1/4]-1)/4, 10, 120] // First (* Jean-François Alcover, Feb 13 2013 *)

Prog

(Sage)
def A190407(b): # Generate the constant with b bits of precision
    return N(sum([(1/2)^(2*k^2+1) for k in range(1, b)]), b)
A190407(415) # Danny Rorabaugh, Mar 26 2015
(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2)
(th3(1/4)-1)/4 \\ Charles R Greathouse IV, Jun 06 2016

Crossrefs

Cf. A058331, A190404, A190405, A190406.

Sequence in context: A265989 A225847 A021375 * A057052 A362533 A346406

Adjacent sequences: A190404 A190405 A190406 * A190408 A190409 A190410

Keyword

nonn,cons,easy

Author

Clark Kimberling, May 10 2011

Status

approved