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A299998
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Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)/2).
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6
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1, 6, 4, 1, 6, 3, 2, 5, 6, 0, 6, 5, 5, 1, 5, 3, 8, 6, 6, 2, 9, 3, 8, 4, 2, 7, 7, 0, 2, 2, 5, 4, 2, 9, 4, 3, 4, 2, 2, 6, 0, 6, 1, 5, 3, 7, 9, 5, 6, 7, 3, 9, 7, 4, 7, 8, 0, 4, 6, 5, 1, 6, 2, 2, 3, 8, 0, 1, 4, 4, 6, 0, 3, 7, 3, 3, 3, 5, 1, 7, 7, 5, 6, 0, 0, 3, 6, 4, 1, 7, 1, 6, 2, 3, 3, 5, 9
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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 A010054 of the triangular numbers A000217.
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LINKS
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FORMULA
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Equals 1 + A190405 (as a decimal number).
Equals Product{k>=1} (1 - 1/2^(2*k))/(1 - 1/2^(2*k-1)). - Amiram Eldar, Aug 13 2020
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EXAMPLE
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1.641632560655153866293842770225429434226061537956739747804651622380144603733...
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MATHEMATICA
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RealDigits[QPochhammer[1/4, 1/4]/QPochhammer[2, 1/4], 10, 100][[1]] (* Amiram Eldar, Aug 13 2020 *)
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PROG
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(PARI) default(realprecision, 200); suminf(k=0, 2^(-k*(k+1)/2))
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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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