A079387 - OEIS

%I #15 Jan 20 2019 23:17:34

%S 2,3,3,7,5,7,3,37,7,3,149,19,41,17,7,3,11,2,11,17,23,19,11,5,3,5,3,3,

%T 5,2,5,2,23,7,13,13,19,37,7,41,29,11,2,11,3,3,7,7,3,23,7,19,11,11,17,

%U 11,7,5,7,5,5,3,5,2,5,7,19,31,19,17,7,5,11,3,3,3,103,853,211,23,19,17,11,7,5

%N Costé prime expansion of sqrt(3) - 1.

%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="/A079387/b079387.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 := 200: 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(3)-1);

%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[3] - 1] (* _G. C. Greubel_, Jan 20 2019 *)

%Y Cf. A079388, A079389, 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