A261814 a(n) = smallest initial value s such that n is in the Collatz trajectory of s (s is not regarded as part of its trajectory).

2, 3, 6, 3, 3, 12, 9, 3, 18, 3, 7, 24, 7, 9, 30, 3, 7, 36, 25, 7, 42, 7, 15, 48, 33, 7, 54, 9, 19, 60, 27, 21, 66, 7, 15, 72, 43, 25, 78, 7, 27, 84, 57, 19, 90, 15, 27, 96, 43, 33, 102, 7, 15, 108, 73, 37, 114, 19, 39, 120, 27, 27, 126, 21, 43, 132, 39, 45

Offset

1,1

Comments

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

For even n obviously a(n) <= 2n, because the halving step would reach n. - R. J. Mathar, Nov 27 2015

Links

Michel Lagneau, Table of n, a(n) for n = 1..5000

Example

a(1)=2 because the number 1 is in the trajectory 2 -> 1;
a(2)=3 because the number 2 is in the trajectory 3 -> 10 -> 5 -> ... -> 2 -> 1;
a(3)=6 because the number 3 is in the trajectory 6 -> 3 -> 10 -> ... -> 1;
a(4)=3 because the number 4 is in the trajectory 3 -> 10 -> 5 -> ... -> 4 -> 2 -> 1.

Maple

Collatz := proc(n)
    if type(n, 'even') then
        n/2;
    else
        3*n+1 ;
    end if;
end proc:
CollatzTrj := proc(x, membSrch)
    local t;
    t := x ;
    while t <> 1 do
        t := Collatz(t) ;
        if t = membSrch then
            return true ;
        end if;
    end do:
    return false;
end proc:
A261814 := proc(n)
    for x from 2 do
        if CollatzTrj(x, n) then
            return x;
        end if;
    end do;
end proc: # R. J. Mathar, Nov 27 2015

Crossrefs

Cf. A006577, A260303, A260389.

Sequence in context: A245886 A224504 A216059 * A240965 A084228 A328571

Adjacent sequences: A261811 A261812 A261813 * A261815 A261816 A261817

Keyword

nonn

Author

Michel Lagneau, Nov 22 2015

Status

approved