A350747 Number of iterations required to terminate trajectory mapping described in A349824.

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}.

Links

Table of n, a(n) for n=0..72.

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

Cf. A349824, A001414, A001222.

Sequence in context: A005076 A296182 A019863 * A243456 A246772 A198820

Adjacent sequences: A350744 A350745 A350746 * A350748 A350749 A350750

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