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.

Showing 1-2 of 2 results.

A132346 Number of nonisomorphic arrangements of n lines in the real projective plane, including the arrangement where all the lines pass through a common point.

Original entry on oeis.org

1, 1, 1, 2, 3, 5, 18
Offset: 0

Views

Author

N. J. A. Sloane, Nov 09 2007

Keywords

Comments

See the illustration of initial terms in A048872.

References

  • J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
  • B. Grünbaum, Arrangements and Spreads. American Mathematical Society, Providence, RI, 1972, p. 4.

Crossrefs

Equals A048872 + 1. Cf. A003036, A048873. Different from A121510.

A224254 Full cycle lengths in the Collatz (3x+1) problem when the negative integers are used.

Original entry on oeis.org

2, 2, 2, 2, 5, 2, 5, 2, 5, 5, 2, 2, 5, 5, 2, 2, 18, 5, 5, 5, 18, 2, 18, 2, 18, 5, 5, 5, 2, 2, 18, 2, 18, 18, 5, 5, 18, 5, 2, 5, 18, 18, 2, 2, 18, 18, 5, 2, 18, 18, 5, 5, 2, 5, 18, 5, 2, 2, 2, 2, 18, 18, 5, 2, 2, 18, 18, 18, 2, 5, 2, 5, 18, 18, 5, 5, 2, 2, 2, 5, 5
Offset: 1

Views

Author

Michel Lagneau, Apr 02 2013

Keywords

Comments

There are other cycles of lengths 2, 5 and 18 if negative integers are used. In Z, it is conjectured that the five values of cycle are 1, 2, 3, 5 and 18 (see A121510).

Examples

			a(1) = 2 because the cycle -1 -> -2 -> -1... contains 2 distinct terms;
a(5) = 5 because the cycle -5 -> -14 -> -7->-20 -> -5 ... contains 5 distinct terms;
a(17) = 18 because the cycle -17 -> -50 -> -25->-74 -> -37 -> -110 -> -55->-164 -> -82 -> -41 -> -122->-61 -> -182 -> -91 -> -272->-136 -> -68 -> -34 -> -17... contains 18 distinct terms.

Links

Crossrefs

Cf. A121510, A224166, A224183.

Programs

  • Python
    import sympy
def A224254(n):
  return next(sympy.cycle_length(lambda x:3*x+1 if x%2 else x//2,-n))[0] # Pontus von Brömssen, Jan 24 2021

Extensions

Data corrected by Pontus von Brömssen, Jan 24 2021
Showing 1-2 of 2 results.

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

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