A242072 Decimal expansion of the value of the continued fraction constructed from Mersenne primes.
3, 1, 8, 2, 4, 8, 1, 5, 8, 4, 0, 5, 8, 4, 4, 8, 6, 9, 4, 2, 5, 9, 6, 2, 0, 2, 7, 4, 8, 1, 4, 0, 6, 9, 4, 2, 4, 3, 8, 0, 6, 2, 3, 6, 5, 6, 4, 0, 6, 8, 4, 8, 8, 4, 0, 6, 7, 6, 7, 6, 0, 6, 3, 2, 2, 1, 4, 7, 6, 7, 3, 0, 9, 2, 5, 7, 5, 8, 7, 9, 1, 0, 3, 9, 7, 4, 5, 6, 9, 5, 4, 1, 9, 5, 2, 5, 5, 7, 0, 3, 7, 4, 5, 3
Offset: 0
Examples
0.318248158405844869425962027481406942438062365640684884...
Links
- Jean-Francois Alcover, Table of n, a(n) for n = 0..103
- C. K. Caldwell, Mersenne Primes
- Eric Weisstein's MathWorld, Mersenne Prime
- Marek Wolf, "Continued fractions constructed from prime numbers" arXiv:1003.4015 [math.NT] Sep 26 2010, p. 12.
Programs
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Mathematica
(* The first 9 Mersenne primes suffice to get 104 correct digits *) MersennePrimes = Select[2^Prime[Range[18]] - 1, PrimeQ]; u = FromContinuedFraction[Join[{0}, MersennePrimes]]; RealDigits[u, 10, 104] // First