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A319015
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Decimal expansion of Sum_{k>=0} 1/2^(k^2).
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2
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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
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OFFSET
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1,2
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COMMENTS
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The binary expansion is the characteristic function of the squares (A010052).
This constant is transcendental (Nesterenko, 1996). - Amiram Eldar, Apr 30 2020
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LINKS
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FORMULA
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Equals (1 + theta_3(1/2))/2, where theta_3 is the Jacobi theta function.
Equals 1 + Sum_{k>=1) lambda(k)/(2^k - 1), where lambda is the Liouville function (A008836). - Amiram Eldar, Apr 30 2020
Equals 1 + Sum_{k>=1} floor(sqrt(k))/2^(k+1) (Shamos, 2011, p. 4). - Amiram Eldar, Mar 12 2024
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EXAMPLE
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1.5644684136059385793347... = (1.1001000010000001000000001...)_2.
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0 1 4 9 16 25
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MATHEMATICA
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RealDigits[(1 + EllipticTheta[3, 0, 1/2])/2, 10, 110] [[1]]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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