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A191504
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Decimal expansion of the number 1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... )))))))))), where coefficients > 1 are the primes.
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3
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6, 6, 2, 0, 9, 4, 2, 5, 1, 7, 8, 5, 1, 0, 3, 7, 5, 8, 8, 1, 2, 3, 1, 8, 1, 0, 8, 9, 8, 4, 1, 6, 3, 6, 8, 6, 0, 7, 3, 3, 8, 5, 4, 7, 7, 0, 8, 1, 2, 4, 4, 6, 6, 3, 2, 3, 2, 0, 1, 9, 3, 1, 2, 8, 5, 5, 4, 0, 4, 3, 3, 9, 7, 6, 2, 2, 7, 7, 5, 4, 4, 4, 2, 4, 3, 0, 1, 4, 4, 7, 8, 9, 8, 2, 6, 0, 6, 5, 3, 6, 4, 9, 6, 5, 7, 8, 9, 6, 6, 2, 5, 0, 5, 5, 9, 7, 2, 7, 0, 9, 8, 8, 0, 2, 6, 5, 0, 9, 6, 6, 2, 5, 0, 4, 3, 3, 9, 0, 2, 1, 4, 6, 5, 0, 2, 1, 7, 6, 8, 7, 3, 6, 2, 5, 8, 7, 7, 5, 5, 2, 8, 4, 8, 6, 8, 5, 5, 1, 1, 9, 9, 3, 4, 9, 5, 5, 7, 6, 4, 2, 3, 2, 5, 4, 8, 2, 2, 7, 5
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OFFSET
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0,1
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COMMENTS
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The number can be written 1/(1+s(0)) with s(k)=prime(k)/(1+s(k+1)), prime(0):=1. Asymptotically, s(k) ~ sqrt(prime(k)).
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LINKS
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FORMULA
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1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... ))))))))))
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EXAMPLE
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0.6620942517851037588123181089841636860733854770812446632320193128554043...
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MATHEMATICA
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N[Fold[#2/(1 + #1) &, 0, Join[Reverse@Prime@Range@180000, {1, 1}]], 111] (* Robert G. Wilson v, Jun 16 2011 *)
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PROG
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(PARI) default(realprecision, 80); s=sqrt(p=1e6); while(p=precprime(p-1), s=p/(1+s)); eval(vecextract(Vec(Str((1+s)/(2+s))), "3..-2")) \\ M. F. Hasler, Jun 16 2011
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Values corrected upon observation by R. J. Mathar, Jun 16 2011
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STATUS
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approved
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