cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Ralf Stephan, Nov 24 2010

Keywords

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.

Crossrefs

Cf. A172143.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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