A074769 Least k such that the number of steps to reach 1 starting with k and iterating the Collatz process equals k/n, or -1 if no such k exists.

5, 2, 21, 16, 40, 120, 238, 96, 261, 150

Offset

1,1

Comments

Least k such that A006577(k) = k/n, or -1.

By definition, k is divisible by n. - Ralf Stephan, Sep 01 2003

The sequence (with question marks for the unknown values) begins 5, 2, 21, 16, 40, 120, 238, 96, 261, 150, ?, 288, 767, 2002, 405, 160, 170, 2016, ?, 1980, 693, 1078, 2645, ?, 625, 650, ?, 784, ?, ...

For n in {11, 19, 24, 27, 29, 35, 37, 38, 45, 46}, if k exists, it is greater than 10^7. - David A. Corneth, Jan 29 2022

Links

Table of n, a(n) for n=1..10.

Example

a(3) = 21 as the Collatz trajectory of 21 is 21 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1 which takes 7 steps. 21/7 = 3 and 21 is the smallest k such that k/3 is the number of steps in the Collatz trajectory. - David A. Corneth, Jan 29 2022

Prog

(PARI) a(n)=if(n<0, 0, k=n; while(abs(if(k<0, 0, s=k; c=1; while((1-(s%2))*s/2+(s%2)*(3*s+1)>1, s=(1-(s%2))*s/2+(s%2)*(3*s+1); c++); c)-k/n)>0, k=k+n); k)

Crossrefs

Cf. A006577.

Sequence in context: A191667 A130329 A096035 * A036165 A246798 A367675

Adjacent sequences: A074766 A074767 A074768 * A074770 A074771 A074772

Keyword

nonn

Author

Benoit Cloitre, Sep 29 2002

Extensions

More terms from Ralf Stephan, Sep 01 2003

a(1) = 5 prepended by David A. Corneth, Jan 29 2022

Edited by N. J. A. Sloane, Jan 29 2022

Status

approved