A260303 For the Collatz (3x+1) iteration starting at k, the sequence lists the smallest k such that prime(n) belongs to the trajectory of k, or 0 if no such k exists.

3, 6, 3, 9, 7, 7, 7, 25, 15, 19, 27, 43, 27, 57, 27, 15, 39, 27, 39, 27, 97, 105, 55, 39, 129, 39, 27, 27, 145, 75, 169, 87, 27, 123, 99, 201, 123, 217, 27, 115, 79, 241, 127, 171, 87, 235, 187, 297, 151, 135, 27, 159, 321, 27, 171, 27, 79, 361, 369, 187, 27, 195

Offset

1,1

Comments

The initial term k is not counted as an element of the trajectory.

Links

Michel Lagneau, Table of n, a(n) for n = 1..1000

Example

a(1)=3 because 2 = prime(1) in the trajectory 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1;
a(2)=6 because 3 = prime(2) is  in the trajectory 6 -> 3 -> 10 -> ... -> 1;
a(3)=3 because 5 = prime(3) is in the trajectory 3 -> 10 -> 5 -> ... -> 1;
a(4)=9 because 7 = prime(4) is in the trajectory 9 -> 28 -> 14 -> 7 -> ... -> 1.

Maple

with(numtheory):
for n from 1 to 100 do:
jj:=0:
for k from 1 to 10^6 while(jj=0) do:
lst:={}:m:=k:ii:=0:it:=10^6:
   for i from 1 to it while(ii=0) do:
    if irem(m, 2)=0
    then
    m:=m/2:
    else m:=3*m+1:
    fi:
    lst:=lst union {m}:
     if m=1
     then
     ii:=1:
     else
     fi:
   od:
    n0:=nops(lst):
    for j from 1 to n0 while(jj=0)do:
     if ithprime(n)=lst[j]
     then
     jj:=1:
     else fi:
    od:
     if jj=1 then printf(`%d, `, k):
     else fi:
    od:od:

Crossrefs

Cf. A000040, A006577.

Sequence in context: A065231 A351102 A019918 * A055373 A263333 A328371

Adjacent sequences: A260300 A260301 A260302 * A260304 A260305 A260306

Keyword

nonn

Author

Michel Lagneau, Nov 21 2015

Status

approved