

A299351


For x=n, iterate the map x > Product_{k is a prime dividing x} (k + 1), a(n) is the number of steps to see a repeated term for the first time.


2



3, 2, 2, 3, 2, 4, 3, 3, 3, 2, 1, 4, 3, 3, 3, 3, 2, 4, 3, 4, 3, 3, 2, 3, 4, 3, 3, 4, 3, 4, 3, 3, 3, 3, 2, 5, 4, 4, 3, 4, 3, 4, 3, 3, 3, 3, 2, 4, 3, 3, 4, 3, 2, 3, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 2, 6, 5, 3, 4, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3
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OFFSET

2,1


COMMENTS

It appears that all n end in the orbit (3,4) or the fixed point 12, verified to n=10^8.
Let p,q,r,... be primes that increased by 1 become a power of 2 (the Mersenne primes, A000668). Then for n = p^a*q^b*r^c*..., a,b,c,...>=1 > (p+1)*(q+1)*(r+1)... = 2^e, e>=2 > (2+1)=3.
The case 3^k, k>=2 first yields 4 and then 3: > (3+1)=4=2^2 > (2+1)=3.
It appears that these are the only ones entering the orbit (3,4), all other n end in the fixed point 12.


LINKS

Lars Blomberg, Table of n, a(n) for n = 2..10000


EXAMPLE

For n=2: 2 > (2+1)=3 > (3+1)=4=2^2 > (2+1)=3; 3 is repeated so a(2)=3.
For n=19: 19 > (19+1)=20=2^2*5 > (2+1)*(5+1)=18=2*3^2 > (2+1)*(3+1)=12=2^2*3 > (2+1)*(3+1)=12; 12 is repeated so a(19)=4.


CROSSREFS

Cf. A299352.
Sequence in context: A305534 A248138 A049234 * A294299 A125504 A243929
Adjacent sequences: A299348 A299349 A299350 * A299352 A299353 A299354


KEYWORD

nonn


AUTHOR

Lars Blomberg, Feb 07 2018


STATUS

approved



