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A065443
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Decimal expansion of Sum_{k=1..inf} 1/(2^k-1)^2.
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11
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1, 1, 3, 7, 3, 3, 8, 7, 3, 6, 3, 4, 4, 1, 9, 6, 5, 9, 6, 6, 9, 6, 9, 1, 3, 3, 6, 8, 3, 0, 1, 3, 4, 7, 5, 8, 3, 8, 3, 0, 8, 4, 9, 3, 0, 9, 8, 1, 3, 8, 8, 2, 8, 8, 2, 0, 7, 0, 4, 4, 9, 3, 3, 1, 0, 4, 6, 4, 9, 3, 8, 6, 2, 5, 2, 0, 4, 0, 8, 9, 9, 8, 0, 0, 0, 5, 4, 0, 5, 0, 9, 0, 4, 2, 3, 5, 1, 3, 1, 1, 8, 4, 0, 3, 6
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OFFSET
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1,3
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
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LINKS
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FORMULA
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Equals Sum_{k>=1} k/(2^(k+1)-1).
Equals Sum_{n >= 1} q^(n^2)*( (n - 1) + q^n - (n - 1)*q^(2*n) )/(1 - q^n)^2 evaluated at q = 1/2 (see A065608). - Peter Bala, Oct 16 2022
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EXAMPLE
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1.1373387363441965966969133683013475838308493098...
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MATHEMATICA
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RealDigits[ NSum[1/(2^k - 1)^2, {k, 1, Infinity}, PrecisionGoal -> 40, AccuracyGoal -> 40, WorkingPrecision -> 500, NSumTerms -> 50, NSumExtraTerms -> 50]][[1]] (* Peter Bertok (peter(AT)bertok.com), Dec 04 2001 *)
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PROG
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(PARI) { default(realprecision, 2080); x=suminf(k=1, 1/(2^k - 1)^2); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065443.txt", n, " ", d)) } \\ Harry J. Smith, Oct 19 2009
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Peter Bertok (peter(AT)bertok.com), Dec 04 2001
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STATUS
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approved
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