A079366 -id:A079366 - 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

A080348 Costé prime expansion of Catalan's constant.

Original entry on oeis.org

2, 2, 2, 5, 2, 5, 3, 7, 11, 5, 11, 7, 23, 13, 11, 3, 5, 2, 7, 5, 3, 7, 5, 13, 43, 43, 29, 17, 5, 2, 19, 11, 5, 3, 7, 5, 5, 3, 7, 7, 11, 3, 3, 7, 11, 2, 13, 7, 19, 13, 11, 11, 5, 3, 3, 3, 7, 7, 11, 3, 3, 7, 13, 37, 17, 7, 3, 7, 5, 5, 5, 2, 11, 5, 5, 5, 5, 2, 5, 5, 37, 7, 157, 53, 1361, 131, 107

Offset: 0

Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 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).

A. Costé, Sur un système fibré lié à la suite des nombres premiers, Exper. Math., 11 (2002), 383-405.

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

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(Catalan);

A079370 Records in A079369.

Original entry on oeis.org

2, 3, 5, 11, 17, 37, 53, 73, 79, 277, 2903, 9463, 24631, 202049

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079369.

N. J. A. Sloane, Transforms

Cf. A079369, A079371, A079366-A079368.

A079369 = Cases[Import["https://oeis.org/A079369/b079369.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079369], i++,
  If[A079369[[i]] > l, l = A079369[[i]]; AppendTo[a, l]]];
a (* Robert Price, Mar 14 2020 *)

a(13)-a(14) from Robert Price, Mar 14 2020

A079371 Where records occur in A079369.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 19, 23, 25, 35, 36, 42, 976, 977

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079369.

N. J. A. Sloane, Transforms

Cf. A079369, A079370, A079366-A079368.

A079369 = Cases[Import["https://oeis.org/A079369/b079369.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079369], i++,
  If[A079369[[i]] > l, l = A079369[[i]]; AppendTo[a, i]]];
a (* Robert Price, Mar 14 2020 *)

a(13)-a(14) from Robert Price, Mar 14 2020

A079373 Records in A079372.

Original entry on oeis.org

3, 5, 17, 29, 31, 37, 53, 97, 211, 1489, 1531, 1741, 4217, 12373, 12953, 14939, 34667, 180797

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079372.

N. J. A. Sloane, Transforms

Cf. A079372, A079374, 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, l]]];
a (* Robert Price, Mar 14 2020 *)

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

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

A079376 Records in A079375.

Original entry on oeis.org

2, 3, 5, 19, 29, 53, 149, 491, 1877, 52769

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079375.

N. J. A. Sloane, Transforms

Cf. A079375, A079377, A079366-A079368.

A079375 = Cases[Import["https://oeis.org/A079375/b079375.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079375], i++,
  If[A079375[[i]] > l, l = A079375[[i]]; AppendTo[a, l]]];
a (* Robert Price, Mar 14 2020 *)

a(8)-a(10) from Robert Price, Mar 14 2020

A079377 Where records occur in A079375.

Original entry on oeis.org

1, 3, 5, 7, 9, 10, 11, 100, 263, 265

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079375.

N. J. A. Sloane, Transforms

Cf. A079375, A079376, A079366-A079368.

A079375 = Cases[Import["https://oeis.org/A079375/b079375.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079375], i++,
  If[A079375[[i]] > l, l = A079375[[i]]; AppendTo[a, i]]];
a (* Robert Price, Mar 14 2020 *)

a(8)-a(10) from Robert Price, Mar 14 2020

A079379 Records in A079378.

Original entry on oeis.org

2, 5, 7, 11, 13, 79, 383, 1087, 2833, 12497

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079378.

N. J. A. Sloane, Transforms

Cf. A079378, A079380, A079366-A079368.

A079378 = Cases[Import["https://oeis.org/A079378/b079378.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079378], i++,
  If[A079378[[i]] > l, l = A079378[[i]]; AppendTo[a, l]]];
a (* Robert Price, Mar 14 2020 *)

a(8)-a(10) from Robert Price, Mar 14 2020

cp's OEIS Frontend

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

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A079389 Where records occur in A079387.

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A080348 Costé prime expansion of Catalan's constant.

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A079370 Records in A079369.

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A079371 Where records occur in A079369.

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A079373 Records in A079372.

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A079374 Where records occur in A079372.

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A079376 Records in A079375.

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