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

0, 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

0,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Mathematica

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

Prog

(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

Crossrefs

Cf. A000668, A173898 (decimal expansion), A209600.

Sequence in context: A022177 A015133 A040202 * A040201 A179948 A160495

Adjacent sequences: A209598 A209599 A209600 * A209602 A209603 A209604

Keyword

nonn,cofr

Author

N. J. A. Sloane, Mar 10 2012

Extensions

a(0)=0 prepended by Andrew Howroyd, Nov 30 2025

Status

approved