A079373 -id:A079373 - cp's OEIS frontend

A079372 Costé prime expansion of sqrt(2) - 1.

3, 5, 5, 17, 11, 3, 29, 31, 29, 13, 7, 37, 7, 5, 3, 5, 5, 5, 11, 17, 7, 13, 13, 17, 11, 5, 3, 31, 31, 53, 41, 97, 47, 19, 17, 17, 41, 71, 29, 11, 211, 23, 79, 17, 5, 7, 23, 17, 5, 3, 11, 5, 2, 17, 7, 17, 5, 2, 23, 11, 3, 3, 5, 5, 3, 3, 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).

Nathaniel Johnston, Table of n, a(n) for n = 0..5000
A. Costé, Sur un système fibré lié à la suite des nombres premiers, Exper. Math., 11 (2002), 383-405.

Cf. A079373, A079374, 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 50 do p := P(y); t1 := [op(t1),p]; y := p*y-1; od; t1; end; F(sqrt(2)-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[2] -1] (* G. C. Greubel, Jan 20 2019 *)

A079374 Where records occur in A079372.

Original entry on oeis.org

1, 2, 4, 7, 8, 12, 30, 32, 41, 237, 238, 497, 688, 1080, 1544, 1619, 2757, 3187

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079372.

N. J. A. Sloane, Transforms

Cf. A079372, A079373, A079366-A079368.

A079372 = Cases[Import["https://oeis.org/A079372/b079372.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079372], i++,
  If[A079372[[i]] > l, l = A079372[[i]]; AppendTo[a, i]]];
a (* Robert Price, Mar 14 2020 *)

a(10) - a(18) from Nathaniel Johnston, Apr 25 2011

cp's OEIS Frontend

A079372 Costé prime expansion of sqrt(2) - 1.

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