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A173643
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Positive numbers of form 2^m - 2^l - 3*2^k (A172233) divisible by 9, divided by 9.
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0
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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
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OFFSET
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1,2
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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