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%I #17 Jan 21 2019 10:07:50
%S 2,5,7,5,5,2,11,5,2,13,11,5,5,5,5,2,5,3,5,11,2,79,37,11,5,3,7,17,59,
%T 23,11,2,17,7,3,7,7,383,337,67,13,19,47,23,41,17,17,13,67,71,47,17,11,
%U 19,73,53,17,13,37,19,11,5,13,29,43,47,17,5,5,11,3,3,17,5,97,29,11,3,3,3,7
%N Costé prime expansion of (sqrt(5)-1)/2.
%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 G. C. Greubel, <a href="/A079378/b079378.txt">Table of n, a(n) for n = 0..2000</a>
%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((sqrt(5)-1)/2);
%t $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[(Sqrt[5] -1)/2] (* _G. C. Greubel_, Jan 20 2019 *)
%Y Cf. A079379, A079380, A079366, A079367, A079368.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Feb 16 2003
%E More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003
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