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A319016
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Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)).
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2
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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
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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 oblong numbers (A005369).
The Engel expansion of this constant are the powers of 4 (A000302). - Amiram Eldar, Dec 07 2020
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LINKS
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FORMULA
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Equals theta_2(1/2)/2^(3/4), where theta_2 is the Jacobi theta function.
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EXAMPLE
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1.2658700952308663684189... = (1.010001000001000000010000000001...)_2.
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0 2 6 12 20 30
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MATHEMATICA
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RealDigits[EllipticTheta[2, 0, 1/2]/2^(3/4), 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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