|
%I #25 Dec 13 2015 01:43:19
%S 2,5,6,6,5,4,3,8,3,2,1,7,1,3,8,8,8,4,4,4,6,7,5,2,9,1,0,6,3,3,2,2,8,5,
%T 7,5,1,7,8,2,9,7,2,8,2,8,7,0,2,3,1,4,6,4,5,9,6,9,7,3,3,5,2,5,4,6,6,3,
%U 9,9,7,1,9,8,9,0,4,0,0,3,4,6,2,2,3,9,8,8,5,7,1,4,7,8,0,5,6,6,5,8,9,4,1,5,3
%N Decimal expansion of the continued fraction prime(1) + prime(1)/(prime(2) + prime(2)/(prime(3) + prime(3)/(prime(4) + prime(4)/...))).
%C Given a nondecreasing sequence s(n) of natural numbers (such as, in this case, that of primes A000079), the corresponding continued fraction is bf(s(n)) = a(1) + a(1)/(a(2) + a(2)/(a(3) + a(3)/(...))).
%C For the inverse of this mapping of nondecreasing sequences of natural numbers into irrational real numbers greater than 1, see A233582.
%H Stanislav Sykora, <a href="/A233588/b233588.txt">Table of n, a(n) for n = 1..25000</a>
%H S. Sykora, <a href="http://dx.doi.org/10.3247/sl4math13.001">Blazys' Expansions and Continued Fractions</a>, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001
%H S. Sykora, <a href="http://oeis.org/wiki/File:BlazysExpansions.txt">PARI/GP scripts for Blazys expansions and fractions</a>, OEIS Wiki
%F Equals 2 + 2/(3 + 3/(5 + 5/(7 + 7/(11 + 11/(13 + 13/(17 + ...)))))).
%e 2.56654383217138884446752910633228575178297282870231464596973352546639971...
%t RealDigits[ Fold[(#2 + #2/#1) &, 1, Reverse@ Prime@ Range@ 57], 10, 111][[1]] (* _Robert G. Wilson v_, May 22 2014 *)
%o (PARI) See the link.
%Y Cf. A000079 (primes), A233589, A233590, A233591, A233582, A233583, A233584, A233585, A233586, A233587.
%K nonn,cons
%O 1,1
%A _Stanislav Sykora_, Jan 02 2014
|
