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%I #55 Nov 30 2014 15:22:46
%S 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,
%T 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,
%U 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
%N Decimal expansion of the value of the continued fraction constructed from Mersenne primes.
%H Jean-Francois Alcover, <a href="/A242072/b242072.txt">Table of n, a(n) for n = 0..103</a>
%H C. K. Caldwell, <a href="http://www.utm.edu/research/primes/mersenne/index.html">Mersenne Primes</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/MersennePrime.html">Mersenne Prime</a>
%H Marek Wolf, <a href="http://arxiv.org/abs/1003.4015">"Continued fractions constructed from prime numbers"</a> arXiv:1003.4015 [math.NT] Sep 26 2010, p. 12.
%e 0.318248158405844869425962027481406942438062365640684884...
%t (* 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
%Y Cf. A000043 (the main entry for this sequence), A028335, A000668, A247864.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Oct 01 2014
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