cp's OEIS Frontend

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.

%I A287875 #55 Feb 19 2019 14:40:50
%S A287875 1,10,11,11111,101,1011,111,1011,10111,11111,1011,101011,1101,10111,
%T A287875 11101,11111011,10001,10111,10011,11111011,11111,101011,10111,101111,
%U A287875 101011,111001111,11101,10111,11101,1111111,11111,11111,111011,10111,101111,1111110011101,100101
%N 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.
%C A287875 _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
%C A287875 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
%C A287875 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
%H A287875 Chai Wah Wu, <a href="/A287875/b287875.txt">Table of n, a(n) for n = 1..3931</a>
%t A287875 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 *)
%Y A287875 Cf. A230625, A230626, A230627 (where the primes reached are written in base 10).
%K A287875 sign,base
%O A287875 1,2
%A A287875 _N. J. A. Sloane_, Jun 15 2017
%E A287875 Changed the "escape" value from 0 to -1 to be consistent with A195264. - _N. J. A. Sloane_, Jul 27 2017