

A230626


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.


9



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, 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, 6, 0, 2, 0, 4, 4, 3, 2, 2, 0, 4, 4, 3, 0, 5, 2, 2, 2, 3
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OFFSET

2,3


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 bfile 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). 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
See A287878 for the trajectory of 234, which ends at a prime at step 103.  N. J. A. Sloane, Jun 18 2017
See A288894 for the trajectory of 3932.  Sean A. Irvine, Jun 18 2017


LINKS

Sean A. Irvine, Table of n, a(n) for n = 2..10000 (terms 2..3931 from Chai Wah Wu)


EXAMPLE

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.


CROSSREFS

Analogous to A230305.
Cf. A230625, A230627, A080670, A287875, A287878, A288847, A288894.
Sequence in context: A055976 A293305 A316896 * A183700 A275478 A248678
Adjacent sequences: A230623 A230624 A230625 * A230627 A230628 A230629


KEYWORD

sign,base


AUTHOR

N. J. A. Sloane, Oct 27 2013


EXTENSIONS

More terms from Chai Wah Wu, Jul 15 2014


STATUS

approved



