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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 (list; graph; refs; listen; history; text; internal format)
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 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). 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: A046094 A055976 A293305 * A183700 A275478 A248678

Adjacent sequences:  A230623 A230624 A230625 * A230627 A230628 A230629

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Oct 27 2013

EXTENSIONS

More terms from Chai Wah Wu, Jul 15 2014

STATUS

approved

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Last modified February 19 08:38 EST 2018. Contains 299330 sequences. (Running on oeis4.)