A377615 - OEIS

A377615

a(n) is the number of iterations of x -> 2*x + 7 until (# composites reached) = (# primes reached), starting with prime(n).

23, 7, 9, 1, 21, 1, 7, 1, 21, 1, 1, 1, 3, 1, 3, 19, 1, 1, 1, 5, 1, 1, 7, 1, 1, 1, 1, 1, 1, 17, 1, 9, 17, 1, 1, 1, 1, 1, 1, 5, 1, 1, 3, 1, 15, 1, 1, 1, 9, 1, 1, 1, 1, 3, 17, 1, 1, 1, 1, 15, 1, 11, 1, 1, 1, 5, 1, 1, 11, 1, 1, 1, 1, 1, 1, 23, 1, 1, 11, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

For a guide to related sequences, see A377609.

LINKS

Table of n, a(n) for n=1..82.

EXAMPLE

Starting with prime(1) = 2, we have 2*2+7 = 11, then 2*11+7 = 29, etc., resulting in a chain 2, 11, 29, 65, 137, 281, 569, 1145, 2297, 4601, 9209, 18425, 36857, 73721, 147449, 294905, 589817, 1179641, 2359289, 4718585, 9437177, 18874361, 37748729, 75497465 having 24 primes and 24 composites. Since every initial subchain has fewer composites than primes, a(1) = 24-1 = 23. (For more terms from the mapping x -> 2x+7, see A154251.)

MATHEMATICA

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

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

chain[{Prime[1], 2, 7}]

Map[Length[chain[{Prime[#], 2, 7}]] &, Range[100]] - 1

(* Peter J. C. Moses Oct 31 2024 *)

CROSSREFS

Cf. A377609, A154251.

Sequence in context: A158514 A040511 A264350 * A058287 A122706 A096640

Adjacent sequences: A377612 A377613 A377614 * A377616 A377617 A377618

KEYWORD

nonn,new

AUTHOR

Clark Kimberling, Nov 13 2024

STATUS

approved