A377616 - OEIS

%I #8 Nov 21 2024 11:16:26

%S 1,9,5,7,1,3,3,7,5,11,1,3,1,7,1,1,5,1,1,1,1,5,13,5,11,1,3,1,1,1,5,1,1,

%T 31,7,1,1,3,9,3,1,1,1,1,3,5,1,1,3,1,5,3,1,1,3,1,3,1,1,1,1,9,1,1,3,5,1,

%U 5,1,3,3,1,3,1,1,3,1,11,1,5,29,1,1,7

%N a(n) is the number of iterations of x -> 3*x + 2 until (# composites reached) = (# primes reached), starting with prime(n).

%C For a guide to related sequences, see A377609.

%e Starting with prime(1) = 2, we have 2*2+2 = 6; the chain (2,6) has 1 prime and 1 composite. So a(1) = 2-1 = 1.

%t chain[{start_, u_, v_}] := NestWhile[Append[#, u*Last[#] + v] &, {start}, !

%t      Count[#, _?PrimeQ] == Count[#, _?(! PrimeQ[#] &)] &];

%t chain[{Prime[1], 3, 2}]

%t Map[Length[chain[{Prime[#], 3, 2}]] &, Range[100]] - 1

%t (* _Peter J. C. Moses_, Oct 31 2024 *)

%Y Cf. A377609.

%K nonn

%O 1,2

%A _Clark Kimberling_, Nov 17 2024