A377611 a(n) is the number of iterations of x -> 2*x - 5 until (# composites reached) = (# primes reached), starting with prime(n+4).

25, 1, 19, 1, 11, 15, 1, 1, 1, 1, 13, 9, 3, 1, 1, 21, 1, 1, 1, 11, 1, 7, 1, 1, 1, 1, 1, 11, 17, 1, 3, 1, 1, 1, 1, 1, 13, 1, 1, 1, 5, 1, 1, 1, 3, 1, 3, 1, 1, 1, 9, 9, 1, 1, 1, 15, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 3, 3, 1, 3, 1, 1, 1, 7, 1, 1, 3

Offset

1,1

Comments

For a guide to related sequences, see A377609.

Links

Table of n, a(n) for n=1..82.

Example

Starting with prime(5) = 11, we have 2*11-5 = 17, then 2*17-5 = 31, etc., resulting in a chain 11, 17, 29, 53, 101, 197, 389, 773, 1541, 3077, 6149, 12293, 24581, 49157, 98309, 196613, 393221, 786437, 1572869, 3145733, 6291461, 12582917, 25165829, 50331653, 100663301, 201326597 having 13 primes and 13 composites. Since every initial subchain has fewer composites than primes, a(1) = 26-1 = 25.

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[5], 2, -5}]
Map[Length[chain[{Prime[#], 2, -5}]] &, Range[5, 100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)

Crossrefs

Cf. A377609.

Sequence in context: A040645 A040646 A040647 * A126647 A040648 A272129

Adjacent sequences: A377608 A377609 A377610 * A377612 A377613 A377614

Keyword

nonn

Author

Clark Kimberling, Nov 05 2024

Status

approved