A287875 Iterate the map x -> A230625(x) starting at n; sequence gives the first prime (or 1) that is reached, written in base 2, or -1 if no prime is ever reached.

1, 10, 11, 11111, 101, 1011, 111, 1011, 10111, 11111, 1011, 101011, 1101, 10111, 11101, 11111011, 10001, 10111, 10011, 11111011, 11111, 101011, 10111, 101111, 101011, 111001111, 11101, 10111, 11101, 1111111, 11111, 11111, 111011, 10111, 101111, 1111110011101, 100101

Offset

1,2

Comments

David J. Seal found that the number 255987 is fixed by the map described in A230625 (or equally A287874), so a(255987) = -1. (In fact 255987 is the smallest composite number that is fixed.) - N. J. A. Sloane, Jun 15 2017

Also observe that the numbers 1007 and 1269 are mapped to each other by that map, as are the numbers 1503 and 3751 (see the b-file submitted by Chai Wah Wu for A230625). So they are smaller composite values with a(n) = -1, though not fixed. - David J. Seal, Jun 16 2017

a(217) = a(255) = a(446) = a(558) = a(717) = a(735) = a(775) = a(945) = a(958) = -1 since the trajectory either converges to (1007,1269) or to (1503,3751). - Chai Wah Wu, Jun 16 2017

Links

Chai Wah Wu, Table of n, a(n) for n = 1..3931

Mathematica

Table[FromDigits@ IntegerDigits[#, 2] &@ If[n == 1, 1, NestWhile[FromDigits[#, 2] &@ Flatten@ Map[IntegerDigits[#, 2] &, FactorInteger[#] /. {p_, 1} :> {p}] &, n, ! PrimeQ@ # &, {2, 1}]], {n, 37}] (* Michael De Vlieger, Jun 24 2017 *)

Crossrefs

Cf. A230625, A230626, A230627 (where the primes reached are written in base 10).

Sequence in context: A279993 A279598 A280138 * A064795 A273463 A283430

Adjacent sequences: A287872 A287873 A287874 * A287876 A287877 A287878

Keyword

sign,base

Author

N. J. A. Sloane, Jun 15 2017

Extensions

Changed the "escape" value from 0 to -1 to be consistent with A195264. - N. J. A. Sloane, Jul 27 2017

Status

approved