A377612 a(n) is the number of iterations of x -> 2*x + 1 until (# composites reached) = (# primes reached), starting with prime(n).

15, 7, 13, 1, 11, 1, 1, 1, 7, 7, 1, 1, 5, 1, 1, 11, 1, 1, 1, 1, 1, 1, 3, 23, 1, 1, 1, 1, 1, 11, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 19, 1, 3, 1, 1, 1, 1, 1, 1, 1, 7, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 3

Offset

1,1

Comments

For a guide to related sequences, see A377609.

Links

Table of n, a(n) for n=1..83.

Example

Starting with prime(1) = 2, we have 2*2+1 = 5, then 2*5+1 = 11, etc., resulting in a chain 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 983033 having 8 primes and 8 composites. Since every initial subchain has fewer composites than primes, a(1) = 16-1 = 15. (For more terms from the mapping x -> 2x+1, see A055010.)

Mathematica

chain[{start_, u_, v_}] := NestWhile[Append[#, u*Last[#] + v] &, {start}, !
     Count[#, _?PrimeQ] == Count[#, _?(! PrimeQ[#] &)] &];
chain[{Prime[1], 2, 1}]
Map[Length[chain[{Prime[#], 2, 1}]] &, Range[100]] - 1
(* Peter J. C. Moses, Oct 31 2024 *)

Crossrefs

Cf. A377609.

Sequence in context: A240909 A133817 A173447 * A168211 A131876 A325136

Adjacent sequences: A377609 A377610 A377611 * A377613 A377614 A377615

Keyword

nonn

Author

Clark Kimberling, Nov 05 2024

Status

approved