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

Author

M. F. Hasler, Jun 17 2011

Keywords

• nonn
• cons

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.

Examples

			1.959405116020799280441759778412638696681915440489946897372699094159269766...
		

Crossrefs

Cf. A191816 for the continued fraction.

Programs

PARI

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