A079366 - OEIS

%I #23 Aug 07 2019 21:03:06

%S 11,2,11,5,5,2,5,3,17,11,3,3,11,3,3,11,5,3,23,7,5,97,29,37,107,127,29,

%T 17,409,127,11,29,5,67,19,43,31,19,103,59,29,7,3,11,11,5,47,29,11,3,5,

%U 5,3,17,5,29,11,3,3,3,3,5,5,61,151,58889,1877,983,757,163

%N Costé prime expansion of Pi - 3.

%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).

%C Costé prime expansion = Engel expansion where all terms must be primes (cf. A006784).

%H G. C. Greubel, <a href="/A079366/b079366.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.

%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>

%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 50 do p := P(y); t1 := [op(t1),p]; y := p*y-1; od; t1; end; F(Pi-3);

%t $MaxExtraPrecision = 40; 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 <= 70, i++, AppendTo[t1, p = P[y]]; y = p*y-1]; t1]; F[Pi-3] (* _Jean-François Alcover_, Dec 16 2013, translated from Maple *)

%Y Cf. A079367, A079368. Also A079369-A079389.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Feb 15 2003