A221636 Odd numbers n with the property that Collatz (3x+1) trajectory of n contains exactly four terms that are divisible by 5.

7, 9, 11, 13, 17, 19, 29, 37, 39, 49, 51, 59, 67, 69, 75, 77, 79, 87, 89, 99, 101, 117, 119, 131, 139, 149, 157, 179, 181, 187, 197, 209, 211, 219, 237, 241, 247, 249, 261, 269, 277, 279, 281, 309, 317, 321, 329, 349, 357, 367, 369, 371, 397, 419, 421, 439

Offset

1,1

Comments

Many of the numbers have trajectories containing the numbers 40, 20, 10, 5. However, the trajectory of 75 shows another possibility: 75, 340, 170, 85. Is this sequence infinite?

References

R. K. Guy, Unsolved Problems in Number Theory, E16

Links

Table of n, a(n) for n=1..56.

Example

Collatz trajectory of 7 is {7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}. It contains the numbers 40, 20, 10, 5 and no other term divisible by 5. Because no integer < 7 has this property, a(1) = 7.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; fQ[n_] := Module[{c = Collatz[n]}, Length[Select[c, Mod[#, 5] == 0 &]] == 4]; Select[Range[1, 1000, 2], fQ] (* T. D. Noe, Feb 23 2013 *)

Crossrefs

Cf. A070165.

Sequence in context: A347886 A023389 A248963 * A162018 A055741 A103621

Adjacent sequences: A221633 A221634 A221635 * A221637 A221638 A221639

Keyword

nonn

Author

Jayanta Basu, Feb 22 2013

Status

approved