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a(n) = number of iterations of x -> 2 x + 7 to reach a nonprime, starting with prime(n).
5

%I #6 Nov 04 2024 22:30:14

%S 3,2,4,1,2,1,3,1,4,1,1,1,2,1,2,3,1,1,1,2,1,1,3,1,1,1,1,1,1,2,1,2,3,1,

%T 1,1,1,1,1,2,1,1,2,1,3,1,1,1,3,1,1,1,1,2,3,1,1,1,1,2,1,5,1,1,1,3,1,1,

%U 3,1,1,1,1,1,1,3,1,1,2,1,1,1,1,1,1,1

%N a(n) = number of iterations of x -> 2 x + 7 to reach a nonprime, starting with prime(n).

%C See A377120 for a guide to related sequences.

%e prime(3) = 5 -> 17 -> 41 -> 89 -> 185 = 5*37, so a(3) = 4.

%t Table[p = Prime[n]; c = 1; While[p = 2*p + 7; PrimeQ[p], c++]; c, {n, 200}]

%Y Cf. A377120, A377510, A377512, A377513, A377514.

%K nonn

%O 1,1

%A _Clark Kimberling_, Oct 31 2024