

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
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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



