login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191815 Decimal expansion of the number 1+2/(1+3/(1+5/(1+7/(1+11/(...))))), where the numerators are the primes. 3
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, 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, 6, 9, 7, 6, 6, 0, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Inspired by A191504 = 1/(1+1/A191815).
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.
LINKS
EXAMPLE
1.959405116020799280441759778412638696681915440489946897372699094159269766...
PROG
(PARI) default(realprecision, 80); s=sqrt(p=1e6); while( p=precprime(p-1), s=p/(1+s)); return(1+s)
CROSSREFS
Cf. A191816 for the continued fraction.
Sequence in context: A010543 A154830 A201284 * A341430 A341438 A265290
KEYWORD
nonn,cons
AUTHOR
M. F. Hasler, Jun 17 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)