A194428 -id:A194428 - cp's OEIS frontend

A192984 In repeated iterations of function m->m/3 if m == 0 (mod 3), m->4m+a if 4m+a == 0 (mod 3) where a = 1 or 2, a(n) is maximum value achieved if starting from n.

9, 9, 9, 18, 189, 9, 189, 189, 9, 189, 189, 18, 54, 189, 189, 189, 189, 18, 189, 81, 189, 189, 189, 189, 333, 189, 27, 189, 117, 189, 189, 234, 189, 333, 189, 36, 270, 189, 54, 162, 297, 189, 234, 1017, 189, 333, 189, 189, 198, 270, 189, 378, 909, 54

Offset: 1

Michel Lagneau, Aug 25 2011

nonn

Largest value of the trajectory in A194428 .

If a(n) exists (which is the conjecture of A194428) then a(n) must be a multiple of 9, since if a(n) is not divisible by 3 then the next iteration 4*a(n) + 1 or 4*a(n) + 2 would be greater than a(n), while if a(n) was divisible by 3 only once, a(n) = 3x -> x -> 4x+1 or 4x+2 is greater than 3x.

			a(4)=18 since iteration starts: 4, 18,  6,  2,  9,  3,  1,  6,... and 18 is highest value.

Cf. A194428.

with(numtheory):T:=array(1..2000):for n from 1 to 100 do: T[1]:=n:n0:=n:k:=2:for it from 1 to 50 do: z:=irem(n0,3):if z=0 then n0:=n0/3:T[k]:=n0:k:=k+1:else n0:=4*n0 + 1:if irem(n0,3)=0 then T[k]:=n0:k:=k+1:else n0:=n0+1:T[k]:=n0:k:=k+1:fi:fi:od:U:=convert(T,set):n1:=nops(U):maxi:=0:for i from 1 to n1 do: if T[i]> maxi then maxi:=T[i]:else fi:od:printf(`%d, `, maxi):od:

cp's OEIS Frontend

A192984 In repeated iterations of function m->m/3 if m == 0 (mod 3), m->4m+a if 4m+a == 0 (mod 3) where a = 1 or 2, a(n) is maximum value achieved if starting from n.

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