A079387 Costé prime expansion of sqrt(3) - 1.

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, 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, 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

Offset

0,1

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.

Maple

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);

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[Sqrt[3] - 1] (* G. C. Greubel, Jan 20 2019 *)

Crossrefs

Cf. A079388, A079389, A079366, A079367, A079368.

Sequence in context: A208525 A342878 A209574 * A141061 A256447 A076557

Adjacent sequences: A079384 A079385 A079386 * A079388 A079389 A079390

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 16 2003

Extensions

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

Status

approved