A209601 Continued fraction expansion of the sum of the reciprocals of the Mersenne primes (A000668).

1, 1, 14, 1, 2, 3, 1, 3, 2, 5, 194, 1, 14, 1, 2, 2, 2, 40, 1, 1, 1, 4, 4, 1, 5, 1, 4, 4, 1, 3, 18, 1, 1, 7, 28, 2, 5, 1, 4, 13, 3, 2, 2, 3, 9, 2, 3, 6, 1, 3, 3, 3, 3, 1, 1, 3, 8, 1, 184, 3, 2, 1, 1, 1, 3, 1, 1, 12, 1, 10, 2, 3, 2, 6, 18, 1, 1, 9

Offset: 1

Author

N. J. A. Sloane, Mar 10 2012

Keywords

• nonn
• cofr

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000668, A173898, A209600.

Programs

Mathematica

ContinuedFraction[Total[1/(2^MersennePrimeExponent[Range[30]]-1)],80] (* Harvey P. Dale, Aug 09 2021 *)

PARI

isM(p)=my(m=Mod(4,2^p-1));for(i=1,p-2,m=m^2-2);!m
s=1/3;forprime(p=3,default(realprecision)*log(10)\log(2), if(isM(p), s+=1./(2^p-1)));v=contfrac(s);vector(#v-2,i,v[i+1]) \\ Charles R Greathouse IV, Mar 22 2012