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%I #26 Jan 22 2021 16:47:26
%S 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,
%T 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,
%U 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
%N 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.
%C 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)).
%F 1/(1+1/(1+2/(1+3/(1+5/(1+7/(1+11/(1+13/(1+17/(1+19/(1+... ))))))))))
%e 0.6620942517851037588123181089841636860733854770812446632320193128554043...
%t N[Fold[#2/(1 + #1) &, 0, Join[Reverse@Prime@Range@180000, {1, 1}]], 111] (* _Robert G. Wilson v_, Jun 16 2011 *)
%o (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
%Y Cf. A191608.
%K nonn,cons
%O 0,1
%A _Fabrice Auzanneau_, Jun 04 2011
%E Values corrected upon observation by _R. J. Mathar_, Jun 16 2011
%E Corrected and extended by _Max Alekseyev_, Aug 11 2013
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