|
%I #12 Oct 27 2015 03:22:31
%S 5,2,7,5,3,5,11,3,7,5,2,7,79,67,19,29,59,11,5,11,3,47,31,607,419,47,
%T 19,43,37,7,3,29,7,7,5,5,157,53,89,17,5,37,7,11,3,17,5,3,3,29,127,19,
%U 11,11,5,3,13,41,13,11,3,11,11,5,11,3,3,5,2,5,2,5,3,7,3,17,5,11,3,11,17,5,3,5
%N Costé prime expansion of 1/Pi.
%C For x in (0,1], define P(x) = min{p: p prime, 1/x < p}, Phi(x) = P(x)x - 1. Costé prime expansion of x(0) is sequence a(0), a(1), ... given by x(n) = Phi(x(n-1)) (n>0), a(n) = P(x(n)) (n >= 0).
%H A. Costé, <a href="http://www.emis.de/journals/EM/expmath/volumes/11/11.3/Coste383_405.pdf">Sur un système fibré lié à la suite des nombres premiers</a>, Exper. Math., 11 (2002), 383-405.
%p Digits := 500: P := proc(x) local y; y := ceil(evalf(1/x)); if isprime(y) then y else nextprime(y); fi; end; F := proc(x) local y,i,t1; y := x; t1 := []; for i from 1 to 100 do p := P(y); t1 := [op(t1),p]; y := p*y-1; od; t1; end; F(1/Pi);
%Y Cf. A079385, A079386, A079366, A079367, A079368, A080348, A080349.
%K nonn,easy
%O 0,1
%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003
|
