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A079381 Costé prime expansion of Euler's constant gamma (A001620).

%I A079381 #17 Jan 20 2019 23:17:13
%S A079381 2,7,13,19,89,23,11,131,73,43,37,7,11,3,3,3,3,3,5,2,7,61,251,41,13,11,
%T A079381 7,23,29,5,13,11,3,67,29,7,5,5,2,17,5,23,7,11,2,31,29,5,5,5,3,3,5,11,
%U A079381 5,7,7,29,17,5,2,41,13,13,11,199,157,101,37,7,127,29,11,3,3,5,17,5,7,5,2,5
%N A079381 Costé prime expansion of Euler's constant gamma (A001620).
%C A079381 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 A079381 G. C. Greubel, <a href="/A079381/b079381.txt">Table of n, a(n) for n = 0..2000</a>
%H A079381 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 A079381 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(gamma);
%t A079381 $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[EulerGamma] (* _G. C. Greubel_, Jan 20 2019 *)
%Y A079381 Cf. A079382, A079383, A079366-A079368.
%K A079381 nonn,easy
%O A079381 0,1
%A A079381 _N. J. A. Sloane_, Feb 16 2003
%E A079381 More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003