%I #76 Mar 16 2020 19:01:55

%S 0,0,3,0,1,0,1,2,2,0,1,0,1,1,4,0,4,0,3,1,1,0,1,2,4,2,3,0,2,0,2,1,5,1,

%T 7,0,1,1,2,0,2,0,2,3,3,0,1,3,3,1,1,0,1,3,2,6,2,0,1,0,2,2,2,2,3,0,1,2,

%U 6,0,2,0,4,4,3,2,2,0,4,4,3,0,5,2,2,2,3

%N Iterate the map x -> A230625(x) starting at n; sequence gives number of steps to reach a prime, or -1 if no prime is ever reached.

%C _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

%C 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

%C 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). 255987 has several preimages, e.g. a(7^25*31^19) = a(3^28*7^7*19) = a(7^12*31^51) = -1. a(3568) = 74 ending in the prime 318792605899852268194734519209581. - _Chai Wah Wu_, Jun 16 2017

%C See A287878 for the trajectory of 234, which ends at a prime at step 103. - _N. J. A. Sloane_, Jun 18 2017

%C See A288894 for the trajectory of 3932. - _Sean A. Irvine_, Jun 18 2017

%H Sean A. Irvine, <a href="/A230626/b230626.txt">Table of n, a(n) for n = 2..10000</a> (terms 2..3931 from Chai Wah Wu)

%e Starting at 18: 18 = 2*3^2 = 10*11^10 in binary -> 101110 = 46 = 2*23 = 10*10111 -> 1010111 = 87 = 3*29 = 11*11101 -> 1111101 = 125 = 5^3 = 101^11 -> 10111 = 23, prime, taking 4 steps, so a(18) = 4.

%t fn[n_] := FromDigits[Flatten[IntegerDigits[ReplaceAll[FactorInteger[n], {x_, 1} -> {x}], 2]], 2];

%t Map[Length, Table[NestWhileList[fn, n, # != 1 && ! PrimeQ[#] &], {n, 2, 40}], {1}] - 1 (* _Robert Price_, Mar 16 2020 *)

%Y Analogous to A230305.

%Y Cf. A230625, A230627, A080670, A287875, A287878, A288847, A288894.

%K sign,base

%O 2,3

%A _N. J. A. Sloane_, Oct 27 2013

%E More terms from _Chai Wah Wu_, Jul 15 2014