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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 6 22:23 EDT 2020. Contains 333291 sequences. (Running on oeis4.)