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A319016 Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)). 0

%I

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

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

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

%N Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)).

%C The binary expansion is the characteristic function of the oblong numbers (A005369).

%F Equals theta_2(1/2)/2^(3/4), where theta_2 is the Jacobi theta function.

%e 1.2658700952308663684189... = (1.010001000001000000010000000001...)_2.

%e | | | | | |

%e 0 2 6 12 20 30

%t RealDigits[EllipticTheta[2, 0, 1/2]/2^(3/4), 10, 110] [[1]]

%o (PARI) suminf(k=0, 1/2^(k*(k+1))) \\ _Michel Marcus_, Sep 08 2018

%Y Cf. A002378, A005369, A053763, A190405, A299998, A319015.

%K nonn,cons

%O 1,2

%A _Ilya Gutkovskiy_, Sep 07 2018

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Last modified September 21 11:18 EDT 2019. Contains 327253 sequences. (Running on oeis4.)