A377614 - OEIS

%I #4 Nov 17 2024 07:32:27

%S 1,11,1,15,1,17,1,3,1,1,15,17,1,1,1,1,1,13,13,1,19,7,1,1,13,1,15,1,7,

%T 1,1,1,1,9,1,17,1,3,1,1,1,9,1,1,1,1,1,1,1,9,1,1,3,1,1,1,1,5,1,1,3,1,3,

%U 1,5,1,1,1,1,1,1,1,7,7,1,1,1,1,1,7,1,1,1

%N a(n) is the number of iterations of x -> 2*x + 5 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+5 = 9; the chain (2,9) 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], 2, 5}]

%t Map[Length[chain[{Prime[#], 2, 5}]] &, Range[100]] - 1

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

%Y Cf. A377609.

%K nonn

%O 1,2

%A _Clark Kimberling_, Nov 13 2024