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

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

1,1

Comments

For a guide to related sequences, see A377609.

Links

Table of n, a(n) for n=1..85.

Example

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.)

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, A062394.

Sequence in context: A175638 A091900 A222135 * A086318 A244674 A130834

Adjacent sequences: A377619 A377620 A377621 * A377623 A377624 A377625

Keyword

nonn

Author

Clark Kimberling, Nov 20 2024

Status

approved