A190406 Decimal expansion of Sum_{k>=1} (1/2)^S(k-1), where S=A001844 (centered square numbers).

5, 3, 1, 3, 7, 2, 1, 0, 0, 1, 1, 5, 2, 7, 7, 1, 3, 5, 4, 7, 9, 8, 7, 9, 8, 5, 8, 9, 6, 2, 5, 5, 3, 5, 3, 1, 7, 1, 2, 8, 4, 3, 2, 0, 1, 8, 6, 2, 0, 6, 6, 3, 9, 4, 0, 7, 8, 8, 8, 7, 1, 6, 1, 3, 5, 7, 8, 9, 0, 6, 8, 8, 0, 2, 3, 7, 7, 6, 0, 4, 7, 6, 0, 7, 3, 0, 3, 4, 5, 7, 7, 9, 6, 0, 7, 1, 2, 3, 4, 9, 2, 0, 6, 1, 0, 7, 1, 1, 5, 2, 2, 0, 6, 3, 9, 0, 0, 7, 3, 5

Offset

0,1

Comments

See A190404.

Links

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

Formula

a(n) = floor(10^(n+1)*Sum_{j>=0} (1/2)^(2*j*(j+1)+1)) mod 10. - Danny Rorabaugh, Mar 26 2015

Maple

evalf(JacobiTheta2(0, 1/4)/2^(3/2)) ; # R. J. Mathar, Jul 15 2013

Mathematica

(See A190404.)
(* or *) RealDigits[EllipticTheta[2, 0, 1/4]/(2*Sqrt[2]), 10, 120] // First (* Jean-François Alcover, Feb 12 2013 *)

Prog

(Sage)
def A190406(b): # Generate the constant with b bits of precision
    return N(sum([(1/2)^(2*j*(j+1)+1) for j in range(0, b)]), b)
A190406(409) # Danny Rorabaugh, Mar 26 2015
(PARI) th2(x)=x^.25 + 2*suminf(n=1, x^(n+1/2)^2)
th2(1/4)/sqrt(8) \\ Charles R Greathouse IV, Jun 06 2016

Crossrefs

Cf. A190404-A190407.

Sequence in context: A309446 A242439 A176318 * A021657 A154180 A011332

Adjacent sequences: A190403 A190404 A190405 * A190407 A190408 A190409

Keyword

nonn,cons,easy

Author

Clark Kimberling, May 10 2011

Status

approved