A377120 a(n) = number of iterations of x -> 2 x + 3 to reach a nonprime, starting with prime(n) .

4, 1, 4, 3, 1, 3, 2, 2, 1, 2, 1, 1, 1, 3, 6, 2, 1, 1, 6, 1, 2, 1, 1, 2, 5, 1, 1, 1, 1, 3, 2, 1, 5, 2, 1, 1, 2, 1, 3, 3, 1, 1, 1, 2, 4, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 5, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 3, 1, 2, 1, 1, 1, 1, 2, 1

Offset: 1

Author

Clark Kimberling, Oct 31 2024

Keywords

• nonn

Comments

Guide to related sequences:

mapping initial prime sequence

x -> 2x + 1 2 A181697

x -> 2x + 3 2 this sequence

x -> 2x + 5 2 A377510

x -> 2x + 7 2 A377511

x -> 2x - 1 2 A181715

x -> 2x - 3 5 A377512

x -> 2x - 5 11 A377513

x -> 2x - 7 11 A377514

Examples

			prime(1) = 2 -> 7 -> 17 -> 37 -> 77 = 7*11, so a(1) = 4.
		

Crossrefs

Cf. A000040, A181697, A181715, A377510, A377511, A377512, A377513, A377514.

Programs

Mathematica

Table[p = Prime[n]; c = 1; While[p = 2*p + 3; PrimeQ[p], c++]; c, {n, 200}]