A191815 - OEIS

%I #9 Sep 26 2013 06:13:17

%S 1,9,5,9,4,0,5,1,1,6,0,2,0,7,9,9,2,8,0,4,4,1,7,5,9,7,7,8,4,1,2,6,3,8,

%T 6,9,6,6,8,1,9,1,5,4,4,0,4,8,9,9,4,6,8,9,7,3,7,2,6,9,9,0,9,4,1,5,9,2,

%U 6,9,7,6,6,0,2,1

%N Decimal expansion of the number 1+2/(1+3/(1+5/(1+7/(1+11/(...))))), where the numerators are the primes.

%C Inspired by A191504 = 1/(1+1/A191815).

%C Successive applications of x -> 1+1/x  (resp. x -> 1/(1+x)) yield a sequence converging to the Golden ratio (sqrt(5)+1)/2 (resp. (sqrt(5)-1)/2), A001622.

%e 1.959405116020799280441759778412638696681915440489946897372699094159269766...

%o (PARI) default(realprecision,80); s=sqrt(p=1e6); while( p=precprime(p-1), s=p/(1+s)); return(1+s)

%Y Cf. A191816 for the continued fraction.

%K nonn,cons

%O 1,2

%A _M. F. Hasler_, Jun 17 2011