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A350747
Number of iterations required to terminate trajectory mapping described in A349824.
0
0, 1, 0, 0, 8, 0, 9, 0, 7, 4, 8, 0, 3, 0, 7, 8, 7, 0, 6, 0, 1, 2, 2, 0, 5, 2, 1, 0, 0, 0, 0, 0, 6, 0, 7, 6, 4, 0, 6, 7, 3, 0, 5, 0, 2, 1, 6, 0, 8, 1, 5, 4, 5, 0, 3, 7, 6, 3, 11, 0, 9, 0, 10, 8, 11, 5, 9, 0, 9, 6, 6, 0, 10
OFFSET
0,5
COMMENTS
From Wolfdieter Lang, Feb 09 2022: (Start)
Conjecture from A349824: the iteration f: n -> A349824(n) becomes periodic for each n >= 0.
a(n) gives the number of steps from n to reach the first member of the periodic part. There are the two length 2 periods: (33,28) and (28,33). (End)
It appears that the only nonprime values of n for which a(n) = 0 are {0, 27, 28, 30, 33}.
EXAMPLE
For n = 6, the trajectory is 6, 10, 14, 18, 24, 36, 40, 44, 45, 33, ... so a(6) = 9.
For n = 24, the trajectory is 24, 36, 40, 44, 45, 33, ... so a(24) = 5.
MAPLE
with(numtheory): A001222:= n -> bigomega(n):
A001414:= proc(n) local e, j; e:=ifactors(n)[2]; add(e[j][1] * e[j][2], j= 1..nops(e)) end proc :
B := n-> A001414(n) * A001222(n):
g:= proc(n) if isprime(n) or n=0 or n=27 or n=28 or n=30 or n=33 then return 0 else return 1 fi end proc:
F:= proc(n) local v, i; v:=n; if n = 1 then return 1 else if g(n)=0 then return 0 else for i from 0 to 100 do v:= B(v); if v=27 or v=28 or v=30 or v=33 then return i+1; i:=100 fi od fi fi end proc :
Seq(F(n), n=0..100)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary Detlefs, Jan 13 2022
EXTENSIONS
More terms from Jinyuan Wang, Jan 15 2022
Edited by Wolfdieter Lang, Feb 09 2022
STATUS
approved