A230627 Prime reached in A230626, or -1 if no prime is reached.

2, 3, 31, 5, 11, 7, 11, 23, 31, 11, 43, 13, 23, 29, 251, 17, 23, 19, 251, 31, 43, 23, 47, 43, 463, 29, 23, 29, 127, 31, 31, 59, 23, 47, 8093, 37, 83, 61, 127, 41, 179, 43, 467, 463, 23, 47, 83, 127, 467, 113, 173, 53, 47, 23, 179, 241, 127, 59, 349, 61, 179

Offset: 2

Author

N. J. A. Sloane, Oct 27 2013

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. - N. J. A. Sloane, Jun 15 2017

I 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 a(1007) = a(1269) = a(1503) = a(3751) = -1. - 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

See A287878 for the trajectory of 234. - N. J. A. Sloane, Jun 17 2017

See A288894 for the trajectory of 3932. - Sean A. Irvine, Jun 18 2017

The latest information seems to be that for numbers less than 12388, all trajectories either end at a fixed point or in a cycle of length 2. - N. J. A. Sloane, Jul 27 2017

Links

• Sean A. Irvine, Table of n, a(n) for n = 2..10000 (terms 2..3931 from Chai Wah Wu)
• N. J. A. Sloane, Confessions of a Sequence Addict (AofA2017), slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.
• N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

Crossrefs

Base-2 analog to A195264.

Cf. A230625, A230626, A287878.

See A287875 for these same numbers written in binary.

See A288847 for where the values -1 occur.

Programs

Mathematica

fn[n_] := FromDigits[Flatten[IntegerDigits[ReplaceAll[FactorInteger[n], {x_, 1} -> {x}], 2]], 2];
Table[NestWhile[fn, n, # != 1 && ! PrimeQ[#] &], {n, 2, 50}] (* Robert Price, Mar 16 2020 *)

Extensions

More terms from Chai Wah Wu, Jul 15 2014

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