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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. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 23 14:11 EDT 2019. Contains 325254 sequences. (Running on oeis4.)