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

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

1,1

Comments

For a guide to related sequences, see A377609.

Links

Table of n, a(n) for n=1..84.

Example

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.)

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 *)

Crossrefs

Cf. A377609, A198796.

Sequence in context: A040279 A070718 A040277 * A367356 A196924 A109215

Adjacent sequences: A377621 A377622 A377623 * A377625 A377626 A377627

Keyword

nonn

Author

Clark Kimberling, Nov 20 2024

Status

approved