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A248721
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Decimal expansion of Sum_{k>=1} 1/(4^k - 1).
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12
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4, 2, 1, 0, 9, 7, 6, 8, 6, 0, 3, 3, 4, 2, 3, 7, 7, 7, 2, 9, 5, 9, 9, 0, 8, 8, 7, 9, 6, 7, 7, 1, 3, 0, 4, 8, 9, 6, 1, 4, 4, 1, 3, 3, 6, 3, 2, 4, 1, 1, 5, 4, 0, 4, 6, 0, 5, 9, 2, 0, 7, 9, 6, 7, 1, 2, 7, 7, 1, 3, 7, 0, 4, 8, 8, 7, 3, 9, 8, 0, 2, 7, 5, 1, 9, 0, 3, 6, 8, 4, 7, 5, 8, 6, 5, 0, 7, 9, 5, 3, 9, 2, 8, 4, 5
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals Sum_{k>=1} x^(k^2)*(1+x^k)/(1-x^k) where x = 1/4 (the Lambert series evaluated at 1/4). - Joerg Arndt, Jun 03 2020
Equals Sum_{k>=1} d(k)/4^k, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, Jun 22 2020
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EXAMPLE
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0.4210976860334237772959908879677130489614413363241154046059207967127713704887...
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MAPLE
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# second program with faster converging series after Joerg Arndt
evalf( add( (1/4)^(n^2)*(1 + 2/(4^n - 1)), n = 1..13), 105); # Peter Bala, Jan 30 2022
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MATHEMATICA
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x = 1/4; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* after an observation and the formula of Amarnath Murthy, see A073668 *)
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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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