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A173643 Positive numbers of form 2^m - 2^l - 3*2^k (A172233) divisible by 9, divided by 9. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 03:04 EDT 2021. Contains 348099 sequences. (Running on oeis4.)