A079388 -id:A079388 - cp's OEIS frontend

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

N. J. A. Sloane, Feb 16 2003

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).

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.

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

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);

$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 *)

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

A079389 Where records occur in A079387.

Original entry on oeis.org

1, 2, 4, 8, 11, 78, 623, 661, 729, 812, 993, 1088, 1318, 4250, 7041, 7499

Offset: 1

N. J. A. Sloane, Feb 16 2003

nonn

RECORDS transform of A079387.

N. J. A. Sloane, Transforms

Cf. A079387, A079388, A079366, A079367, A079368.

A079387 = Cases[Import["https://oeis.org/A079387/b079387.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079387], i++,
  If[A079387[[i]] > l, l = A079387[[i]]; AppendTo[a, i]]];
a (* Robert Price, Mar 15 2020 *)

More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Dec 06 2005

cp's OEIS Frontend

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

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