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

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

1,2

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

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 *)

Crossrefs

Cf. A377609.

Sequence in context: A160631 A155066 A343480 * A251735 A232811 A380940

Adjacent sequences: A377617 A377618 A377619 * A377621 A377622 A377623

Keyword

nonn

Author

Clark Kimberling, Nov 20 2024

Status

approved