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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

%I #36 Dec 04 2015 23:34:59

%S 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,

%T 19,60,27,21,66,7,15,72,43,25,78,7,27,84,57,19,90,15,27,96,43,33,102,

%U 7,15,108,73,37,114,19,39,120,27,27,126,21,43,132,39,45

%N 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).

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

%C For even n obviously a(n) <= 2n, because the halving step would reach n. - _R. J. Mathar_, Nov 27 2015

%H Michel Lagneau, <a href="/A261814/b261814.txt">Table of n, a(n) for n = 1..5000</a>

%e a(1)=2 because the number 1 is in the trajectory 2 -> 1;

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

%e a(3)=6 because the number 3 is in the trajectory 6 -> 3 -> 10 -> ... -> 1;

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

%p Collatz := proc(n)

%p if type(n,'even') then

%p n/2;

%p else

%p 3*n+1 ;

%p end if;

%p end proc:

%p CollatzTrj := proc(x,membSrch)

%p local t;

%p t := x ;

%p while t <> 1 do

%p t := Collatz(t) ;

%p if t = membSrch then

%p return true ;

%p end if;

%p end do:

%p return false;

%p end proc:

%p A261814 := proc(n)

%p for x from 2 do

%p if CollatzTrj(x,n) then

%p return x;

%p end if;

%p end do;

%p end proc: # _R. J. Mathar_, Nov 27 2015

%Y Cf. A006577, A260303, A260389.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 22 2015

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)