A225866 Numbers n such that the sum of the numbers in the Collatz (3x+1) iteration of n is a perfect square.

1, 3, 5, 33, 60, 245, 304, 372, 1265, 1568, 1756, 1799, 1856, 2409, 2532, 2976, 3100, 3281, 3376, 3394, 3813, 5637, 5972, 6147, 6538, 7213, 7299, 7896, 7966, 8371, 10419, 11526, 13411, 13856, 14168, 15024, 15283, 15709, 16506, 16577, 16916, 19212, 19829, 21372

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

60 is in the sequence because 60 + 30 + 15 + 46 + 23 + 70 + 35 + 106 + 53 + 160 + 80 + 40 + 20 + 10 + 5 + 16 + 8 + 4 + 2 + 1 = 784 = 28^2.

Mathematica

collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; Select[Range[22000], IntegerQ[Sqrt[Total[collatz[#]]]]&]

Crossrefs

Cf. A033493.

Sequence in context: A284379 A372718 A103010 * A332704 A378676 A263295

Adjacent sequences: A225863 A225864 A225865 * A225867 A225868 A225869

Keyword

nonn

Author

Michel Lagneau, May 18 2013

Status

approved