A165509 Continued fraction expansion of sum of reciprocals of primorial numbers: 1/2 + 1/6 + 1/30 + 1/210 + ... .

0, 1, 2, 2, 1, 1, 4, 1, 2, 1, 1, 6, 13, 1, 4, 1, 16, 6, 1, 1, 4, 5, 8, 1, 1, 5, 1, 22, 1, 1, 1, 2, 2, 1, 1, 46, 1, 1, 4, 1, 53, 1, 3, 2, 1, 3, 1, 2, 1, 2, 2, 8, 11, 1, 7, 1, 28, 1, 3, 1, 2, 2, 4, 7, 16, 5, 1, 1, 2, 1, 2, 1, 1, 2, 1, 5, 3, 17, 1, 7, 2, 3, 66, 1, 1, 4, 1, 27, 12, 2, 1, 1, 3, 9, 1, 12, 14, 2, 4

Offset: 0

Author

Harry J. Smith, Sep 21 2009

Keywords

• cofr
• nonn

Examples

			0.705230171791800965147431682... = 0 + 1/(1 + 1/(2 + 1/(2 + 1/(1 + ...))))
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A064648 (decimal expansion).

Programs

Magma

SetDefaultRealField(RealField(100)); ContinuedFraction( (&+[1/(&*[NthPrime(j):j in [1..n]]): n in [1..80]]) ); // G. C. Greubel, Oct 21 2018

Mathematica

ContinuedFraction[Sum[1/Product[Prime[i], {i, n}], {n, 80}], 120] (* G. C. Greubel, Oct 21 2018 *)

PARI

{ allocatemem(932245000); default(realprecision, 21000); p=1; s=x=0; for (k=1, 10^9, p*=prime(k); s+=1.0/p; if (s==x, break); x=s ); x=contfrac(s); for (n=0, 20000, write("b165509.txt", n, " ", x[n+1])) }