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A079384 Costé prime expansion of 2^(1/3) - 1.

%I A079384 #17 Jan 20 2019 23:17:27
%S A079384 5,5,3,3,3,3,3,53,13,29,7,5,11,3,7,5,11,5,7,5,71,67,17,11,5,5,37,11,2,
%T A079384 11,11,3,11,5,5,11,7,11,3,3,3,3,3,3,11,7,7,7,5,23,17,7,17,13,41,53,23,
%U A079384 7,7,5,5,5,5,2,7,3,53,11,3,7,5,2,7,17,17,379,107,41,19,11,5,5,2,5,5,3,11,2,29,11,7,7,13,29,7,53,53,17,11,3
%N A079384 Costé prime expansion of 2^(1/3) - 1.
%C A079384 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 A079384 G. C. Greubel, <a href="/A079384/b079384.txt">Table of n, a(n) for n = 0..2000</a>
%H A079384 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 A079384 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(2^(1/3) - 1);
%t A079384 $MaxExtraPrecision = 500; P[x_]:= Module[{y}, y = Ceiling[1/x]; If[PrimeQ[y], y, NextPrime[y]]]; F[x_] := Module[{y, i, t1}, y = x; t1 = {}; For[i = 1, i <= 100, i++, AppendTo[t1, p = P[y]]; y = p*y - 1]; t1]; F[Surd[2, 3] - 1] (* _G. C. Greubel_, Jan 20 2019 *)
%Y A079384 Cf. A079385, A079386, A079366, A079367, A079368.
%K A079384 nonn,easy
%O A079384 0,1
%A A079384 _N. J. A. Sloane_, Feb 16 2003
%E A079384 More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003