A377613 - OEIS

A377613

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

19, 1, 15, 15, 1, 13, 13, 15, 1, 3, 1, 1, 1, 7, 27, 3, 1, 1, 25, 1, 3, 1, 1, 5, 23, 1, 1, 1, 1, 7, 3, 1, 23, 3, 1, 1, 9, 1, 17, 5, 1, 1, 1, 3, 19, 7, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 1, 21, 1, 3, 1, 19, 1, 1, 1, 1, 3, 1, 3, 3, 1, 1, 1, 3, 3, 1, 17, 1, 3, 1

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OFFSET

1,1

COMMENTS

For a guide to related sequences, see A377609.

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

Starting with prime(1) = 2, we have 2*2+3 = 7, then 2*7+3 = 17, etc.,

resulting in a chain 2, 7, 17, 37, 77, 157, 317, 637, 1277, 2557, 5117, 10237, 20477, 40957, 81917, 163837, 327677, 655357, 1310717, 2621437 having 10 primes and 10 composites. Since every initial subchain has fewer composites than primes, a(1) = 20-1 = 19. (For more terms from the mapping x -> 2x+3, see A154117.)

MATHEMATICA

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

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

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

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

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

CROSSREFS

Cf. A377609, A154117.

Sequence in context: A256642 A040376 A040377 * A040378 A248124 A040379

Adjacent sequences: A377610 A377611 A377612 * A377614 A377615 A377616

KEYWORD

nonn,new

AUTHOR

Clark Kimberling, Nov 13 2024

STATUS

approved