login
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
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
Cf. A191608.
Sequence in context: A098369 A078740 A228708 * A021155 A254245 A218387
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