A377617 - OEIS

%I #8 Nov 21 2024 11:16:55

%S 1,19,13,1,11,3,1,3,17,1,3,1,3,1,1,5,7,1,1,1,13,7,1,3,1,3,5,1,5,1,1,3,

%T 1,3,1,7,1,1,1,7,5,3,5,1,1,3,1,11,1,3,1,1,3,5,1,1,7,1,1,1,3,7,1,3,1,1,

%U 3,1,1,3,3,1,1,5,1,15,5,1,1,13,1,1,5,5

%N a(n) is the number of iterations of x -> 3*x + 4 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 3*2+4 = 10; the chain (2,10) 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, 4}]

%t Map[Length[chain[{Prime[#], 3, 4}]] &, 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