A277121 Numbers that immediately halt Conway's FIBONACCIGAME.

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

Author

Alonso del Arte, Sep 30 2016

Keywords

• nonn

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