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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A275484 Denominators of Conway's FIBONACCIGAME.

Original entry on oeis.org

65, 34, 19, 17, 69, 29, 23, 341, 37, 31, 287, 43, 41, 13, 3
Offset: 1

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Author

Alonso del Arte, Jul 30 2016

Keywords

Comments

Like PRIMEGAME, the object of FIBONACCIGAME is to come up with a listing of the Fibonacci numbers through a process of multiplying integers by fractions to see which produce integers, which are then cycled back through the process.
Notice that there isn't a 1 in this sequence, which means that the progress of the program, starting from a valid input, eventually halts with 2^Fibonacci(n).

References

  • Julian Havil, Nonplussed! Mathematical Proof of Implausible Ideas. Princeton: Princeton University Press (2007): 174.

Crossrefs

Cf. A275483 (numerators), A203363, A000301.

A277121 Numbers that immediately halt Conway's FIBONACCIGAME.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 25, 28, 32, 35, 40, 44, 47, 49, 50, 53, 55, 56, 59, 61, 64, 67, 70, 71, 73, 77, 79, 80, 83, 88, 89, 94, 97, 98, 100, 101, 103, 106, 107, 109, 110, 112, 113, 118, 121, 122, 125, 127, 128, 131, 134, 137, 139, 140, 142, 146, 149, 151, 154, 157, 158
Offset: 1

Views

Author

Alonso del Arte, Sep 30 2016

Keywords

Comments

Like PRIMEGAME, Conway's FIBONACCIGAME uses a list of fractions to come up with a sequence expressed as exponents of powers of 2, the sequence in this case being the Fibonacci numbers (A000045, see A000301).
Unlike PRIMEGAME, FIBONACCIGAME does not have any integers in its list of rational numbers, which means that the process always comes to a halt, sooner or later, depending on the initial value.
Hence this sequence includes all powers of 2 (A000079). Also all primes greater than 43.
However, this sequence includes no multiples of 13 (as they can be handled by 17/65 or 1/13), nor any multiples of 3 (as they're taken care of by 1/3).
Indeed the sequence contains no multiples of 17, 19, 23, 29, 31, 37 either.

Crossrefs

Cf. A275483/A275484.

Programs

  • PARI
    is(n)=gcd(16990599132039,n)==1 && n%65 && n%34 && n%69 && n%341 && n%287 \\ Charles R Greathouse IV, Nov 26 2016
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