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A319016 Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)). 2
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).
The Engel expansion of this constant are the powers of 4 (A000302). - Amiram Eldar, Dec 07 2020
LINKS
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
Sequence in context: A175293 A021083 A244928 * A262096 A011043 A021380
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Sep 07 2018
STATUS
approved

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Last modified March 19 02:46 EDT 2024. Contains 370952 sequences. (Running on oeis4.)