A191815 Decimal expansion of the number 1+2/(1+3/(1+5/(1+7/(1+11/(...))))), where the numerators are the primes.

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

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

Table of n, a(n) for n=1..76.

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

Adjacent sequences: A191812 A191813 A191814 * A191816 A191817 A191818

Keyword

nonn,cons

Author

M. F. Hasler, Jun 17 2011

Status

approved