cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

A377620 a(n) is the number of iterations of x -> 5*x + 4 until (# composites reached) = (# primes reached), starting with prime(n).

Original entry on oeis.org

1, 5, 7, 1, 7, 1, 11, 1, 1, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 5, 1, 1, 7, 3, 1, 13, 1, 1, 1, 7, 1, 7, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 15, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1
Offset: 1

Views

Author

Clark Kimberling, Nov 20 2024

Keywords

Comments

For a guide to related sequences, see A377609.

Examples

			Starting with prime(1) = 2, we have 5*2+4 = 14; the chain (2,14) has 1 prime and 1 composite. So a(1) = 2-1 = 1.

Crossrefs

Cf. A377609.

Programs

  • Mathematica
    chain[{start_, u_, v_}] := If[CoprimeQ[u, v] && start*u + v != start,
   NestWhile[Append[#, u*Last[#] + v] &, {start}, !
      Count[#, ?PrimeQ] == Count[#, ?(! PrimeQ[#] &)] &], {}];
chain[{Prime[1], 5, 4}]
Map[Length[chain[{Prime[#], 5, 4}]] &, Range[1, 100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)

A377621 a(n) is the number of iterations of x -> 6*x - 1 until (# composites reached) = (# primes reached), starting with prime(n).

Original entry on oeis.org

11, 7, 7, 3, 1, 1, 3, 5, 5, 5, 1, 1, 1, 3, 3, 5, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 3, 5, 3, 3, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 9, 3, 1, 1, 5, 7, 1, 9, 1, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 5, 3, 1, 1, 3, 1, 1, 5, 1, 7, 3, 9, 7, 3, 1, 1, 1, 1, 1, 1, 7, 3
Offset: 1

Views

Author

Clark Kimberling, Nov 20 2024

Keywords

Comments

For a guide to related sequences, see A377609.

Examples

			Starting with prime(1) = 2, we have 6*2-1 = 11, then 6*11-1 = 65, etc., resulting in a chain 2, 11, 65, 389, 2333, 13997, 83981, 503885, 3023309, 18139853, 108839117, 653034701 having 6 primes and 6 composites. Since every initial subchain has fewer composites than primes, a(1) = 12-1 = 11. (For more terms from the mapping x -> 6x-1, see A199412.)

Crossrefs

Cf. A377609, A199412.

Programs

  • Mathematica
    chain[{start_, u_, v_}] := If[CoprimeQ[u, v] && start*u + v != start,
   NestWhile[Append[#, u*Last[#] + v] &, {start}, !
      Count[#, ?PrimeQ] == Count[#, ?(! PrimeQ[#] &)] &], {}];
chain[{Prime[1], 6, -1}]
Map[Length[chain[{Prime[#], 6, -1}]] &, Range[1, 100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)

A377622 a(n) is the number of iterations of x -> 6*x - 5 until (# composites reached) = (# primes reached), starting with prime(n).

Original entry on oeis.org

7, 9, 1, 5, 13, 7, 9, 13, 1, 1, 5, 1, 7, 1, 7, 5, 7, 1, 5, 7, 5, 1, 1, 1, 7, 5, 5, 1, 1, 3, 3, 1, 1, 11, 1, 1, 3, 1, 3, 3, 5, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 7, 11, 5, 1, 9, 7, 1, 5, 3, 1, 1, 7, 1, 5, 3, 1, 1, 1, 5, 3, 1, 3, 1, 1, 1, 5, 1, 3, 1
Offset: 1

Views

Author

Clark Kimberling, Nov 20 2024

Keywords

Comments

For a guide to related sequences, see A377609.

Examples

			Starting with prime(1) = 2, we have 6*2-5 = 7, then 6*7-5 = 37, etc., resulting in a chain 2, 7, 37, 217, 1297, 7777, 46657, 279937 having 4 primes and 4 composites. Since every initial subchain has fewer composites than primes, a(1) = 8-1 = 7. (For more terms from the mapping x -> 6x-5, see A062394.)

Crossrefs

Cf. A377609, A062394.

Programs

  • Mathematica
    chain[{start_, u_, v_}] := If[CoprimeQ[u, v] && start*u + v != start,
   NestWhile[Append[#, u*Last[#] + v] &, {start}, !
      Count[#, ?PrimeQ] == Count[#, ?(! PrimeQ[#] &)] &], {}];
chain[{Prime[1], 6, -5}]
Map[Length[chain[{Prime[#], 6, -5}]] &, Range[1, 100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)

A377623 a(n) is the number of iterations of x -> 6*x + 1 until (# composites reached) = (# primes reached), starting with prime(n).

Original entry on oeis.org

15, 5, 5, 3, 3, 13, 7, 1, 5, 1, 1, 3, 1, 1, 7, 1, 1, 7, 1, 1, 3, 1, 7, 1, 1, 9, 5, 3, 1, 1, 1, 5, 3, 1, 1, 5, 1, 1, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 3, 1, 5, 3, 1, 3, 5, 1, 5, 7, 1, 9, 1, 3, 1, 1, 1, 5, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 9
Offset: 1

Views

Author

Clark Kimberling, Nov 20 2024

Keywords

Comments

For a guide to related sequences, see A377609.

Examples

			Starting with prime(1) = 2, we have 6*2+1 = 13, then 6*13+1 = 79, etc., resulting in a chain 2, 13, 79, 475, 2851, 17107, 102643, 615859, 3695155, 22170931, 133025587, 798153523, 4788921139, 28733526835, 172401161011, 1034406966067 having 8 primes and 8 composites. Since every initial subchain has fewer composites than primes, a(1) = 16-1 = 15. (For more terms from the mapping x -> 6x-5, see A198849.)

Crossrefs

Cf. A377609, A198849.

Programs

  • Mathematica
    chain[{start_, u_, v_}] := If[CoprimeQ[u, v] && start*u + v != start,
   NestWhile[Append[#, u*Last[#] + v] &, {start}, !
      Count[#, ?PrimeQ] == Count[#, ?(! PrimeQ[#] &)] &], {}];
chain[{Prime[1], 6, -5}]
Map[Length[chain[{Prime[#], 6, -5}]] &, Range[1, 100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)

A377624 a(n) is the number of iterations of x -> 6*x + 5 until (# composites reached) = (# primes reached), starting with prime(n).

Original entry on oeis.org

17, 5, 1, 3, 9, 11, 15, 1, 1, 3, 7, 5, 5, 7, 1, 1, 5, 1, 1, 7, 5, 5, 9, 1, 5, 1, 1, 9, 3, 13, 1, 1, 5, 9, 1, 11, 5, 7, 1, 1, 1, 13, 5, 7, 9, 1, 1, 1, 3, 1, 1, 9, 3, 3, 1, 3, 7, 1, 9, 1, 1, 1, 5, 5, 1, 13, 1, 3, 9, 3, 1, 1, 3, 17, 1, 1, 5, 1, 3, 9, 1, 5, 5, 1
Offset: 1

Views

Author

Clark Kimberling, Nov 20 2024

Keywords

Comments

For a guide to related sequences, see A377609.

Examples

			Starting with prime(1) = 2, we have 6*2+5 = 17, then 6*17+5 = 107, etc., resulting in a chain 2, 17, 107, 647, 3887, 23327, 139967, 839807, 5038847, 30233087, 181398527, 1088391167, 6530347007, 39182082047, 235092492287, 1410554953727, 8463329722367, 50779978334207 having 9 primes and 9 composites. Since every initial subchain has fewer composites than primes, a(1) = 18-1 = 17. (For more terms from the mapping x -> 6x-5, see A198796.)

Crossrefs

Cf. A377609, A198796.

Programs

  • Mathematica
    chain[{start_, u_, v_}] := If[CoprimeQ[u, v] && start*u + v != start,
   NestWhile[Append[#, u*Last[#] + v] &, {start}, !
      Count[#, ?PrimeQ] == Count[#, ?(! PrimeQ[#] &)] &], {}];
chain[{Prime[1], 6, -5}]
Map[Length[chain[{Prime[#], 6, -5}]] &, Range[1, 100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)
Previous Showing 11-15 of 15 results.

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