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A319015 Decimal expansion of Sum_{k>=0} 1/2^(k^2). 1
1, 5, 6, 4, 4, 6, 8, 4, 1, 3, 6, 0, 5, 9, 3, 8, 5, 7, 9, 3, 3, 4, 7, 2, 9, 2, 7, 4, 2, 7, 2, 4, 7, 5, 6, 6, 2, 3, 0, 6, 2, 5, 8, 2, 6, 9, 9, 7, 0, 4, 3, 9, 0, 4, 6, 4, 4, 4, 5, 0, 5, 5, 9, 6, 0, 2, 8, 4, 8, 0, 1, 3, 3, 1, 7, 9, 5, 7, 8, 4, 0, 6, 6, 5, 9, 1, 3, 0, 6, 4, 0, 1, 6, 2, 4, 6, 9, 1, 4, 8, 4, 4, 7, 4, 0, 2, 4, 7, 1, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The binary expansion is the characteristic function of the squares (A010052).

LINKS

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

FORMULA

Equals (1 + theta_3(1/2))/2, where theta_3 is the Jacobi theta function.

EXAMPLE

1.5644684136059385793347... = (1.1001000010000001000000001...)_2.

                               | |  |    |      |        |

                               0 1  4    9     16       25

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A000290, A002416, A010052, A190405, A299998.

Sequence in context: A187146 A128632 A197490 * A229481 A304490 A155591

Adjacent sequences:  A319012 A319013 A319014 * A319016 A319017 A319018

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, Sep 07 2018

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)