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A319016 Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)). 0
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..110.

FORMULA

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

EXAMPLE

1.2658700952308663684189... = (1.010001000001000000010000000001...)_2.

                               |  |   |     |       |         |

                               0  2   6    12      20        30

MATHEMATICA

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

PROG

(PARI) suminf(k=0, 1/2^(k*(k+1))) \\ Michel Marcus, Sep 08 2018

CROSSREFS

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

Sequence in context: A175293 A021083 A244928 * A262096 A011043 A021380

Adjacent sequences:  A319013 A319014 A319015 * A319017 A319018 A319019

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, Sep 07 2018

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)