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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

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

MAPLE

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:

CROSSREFS

Cf. A194428.

Sequence in context: A141557 A072563 A206011 * A069602 A160761 A082049

Adjacent sequences:  A192981 A192982 A192983 * A192985 A192986 A192987

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 25 2011

STATUS

approved

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Last modified January 23 13:57 EST 2022. Contains 350511 sequences. (Running on oeis4.)