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)).
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
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