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

Author

N. J. A. Sloane, Jun 15 2017

Keywords

• sign
• base

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

Crossrefs

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

Programs

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 *)

Extensions

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