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A262153
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Decimal expansion of Sum_{p prime} 1/(2^p-1), a prime equivalent of the Erdős-Borwein constant.
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1
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5, 1, 6, 9, 4, 2, 8, 1, 9, 8, 0, 5, 6, 4, 0, 3, 8, 4, 2, 4, 0, 5, 1, 6, 6, 0, 8, 4, 7, 9, 8, 5, 6, 2, 7, 7, 9, 7, 8, 5, 4, 6, 9, 4, 7, 9, 1, 3, 0, 9, 1, 2, 4, 1, 6, 5, 0, 2, 8, 0, 2, 4, 5, 8, 7, 1, 2, 3, 8, 0, 7, 5, 3, 4, 1, 1, 3, 6, 0, 3, 7, 7, 1, 9, 8, 1, 8, 0, 2, 8, 0, 5, 4, 0, 2, 5, 0, 8, 8, 2
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OFFSET
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0,1
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COMMENTS
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Erdős was interested in the question whether this constant is irrational. - Amiram Eldar, Apr 30 2020
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REFERENCES
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Paul Erdős, Some of my favourite unsolved problems, in A. Baker, B. Bollobás and A. Hajnal (eds.), A Tribute to Paul Erdős, Cambridge University Press, 1990, p. 470.
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LINKS
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FORMULA
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Equals Sum_{k>=1} omega(k)/2^k, where omega(k) is the number of distinct primes dividing k (A001221). - Amiram Eldar, Apr 30 2020
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EXAMPLE
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0.51694281980564038424051660847985627797854694791309124165028...
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MATHEMATICA
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digits = 100; m0 = 100; dm = 100; s[m_] := s[m] = N[Sum[1/(2^Prime[n]-1), {n, 1, m}], digits+10]; s[m = m0]; Print[{m, s[m]}]; s[m = m + dm]; While[ Print[{m, s[m]}]; RealDigits[ s[m], 10, digits+5] != RealDigits[ s[m - dm], 10, digits+5], m = m + dm]; RealDigits[ s[m], 10, digits] // First
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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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