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

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Feb 16 2003

Keywords

• nonn
• easy

Comments

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).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2000
• A. Costé, Sur un système fibré lié à la suite des nombres premiers, Exper. Math., 11 (2002), 383-405.

Crossrefs

Cf. A079385, A079386, A079366, A079367, A079368.

Programs

Maple

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);

Mathematica

$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 *)

Extensions

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003