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 A191504 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. 3
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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)). LINKS FORMULA 1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... )))))))))) EXAMPLE 0.6620942517851037588123181089841636860733854770812446632320193128554043... MATHEMATICA N[Fold[#2/(1 + #1) &, 0, Join[Reverse@Prime@Range@180000, {1, 1}]], 111] (* Robert G. Wilson v, Jun 16 2011 *) PROG (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. CROSSREFS Cf. A191608. Sequence in context: A098369 A078740 A228708 * A021155 A254245 A218387 Adjacent sequences:  A191501 A191502 A191503 * A191505 A191506 A191507 KEYWORD nonn,cons AUTHOR Fabrice Auzanneau, Jun 04 2011 EXTENSIONS Values corrected upon observation by R. J. Mathar, Jun 16 2011 Corrected and extended by Max Alekseyev, Aug 11 2013 STATUS approved

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Last modified October 28 11:10 EDT 2020. Contains 338054 sequences. (Running on oeis4.)