A173643 Positive numbers of form 2^m - 2^l - 3*2^k (A172233) divisible by 9, divided by 9.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 16, 20, 21, 24, 26, 32, 40, 42, 48, 52, 53, 64, 80, 84, 85, 96, 104, 106, 113, 128, 160, 168, 170, 192, 208, 212, 213, 226, 227, 256, 320, 336, 340, 341, 384, 416, 424, 426, 452, 453, 454, 512, 640, 672, 680

Offset

1,2

Comments

Böhm and Sontacchi show a(n) needs the 3x+1 operator at most twice to reach 1 in the Collatz 3x+1 problem.

Conjecture: Odd part of a(n) is of form [(1/6)*(8^m-(-1)^m-3)*4^k-1]/3, k,m>0.

References

C. Böhm and G. Sontacchi: On the Existence of Cycles of given Length in Integer Sequences like x_(n+1) = x_n/2 if x_n even, and x_(n+1) = 3x_n + 1 otherwise. Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali. Serie VIII 64 (1978), 260-264.

Links

Table of n, a(n) for n=1..55.

Crossrefs

Cf. A172143.

Sequence in context: A067319 A086049 A328208 * A120722 A090811 A162002

Adjacent sequences: A173640 A173641 A173642 * A173644 A173645 A173646

Keyword

nonn

Author

Ralf Stephan, Nov 24 2010

Status

approved