A214897 Conway's subprime Fibonacci sequence: cycle lengths.

1, 10, 11, 18, 19, 56, 136

Offset: 1

Author

Wouter Meeussen, Jul 29 2012

Keywords

• nonn

Comments

Similar to the Fibonacci recursion starting with a pair of positive integers, but each new nonprime term is divided by its least prime factor. The recursion enters a loop of length a(n) after a finite number of steps. Conjecture: the list of loops is complete (checked to [10^5, 10^5]), loops of length a(n) are unique and no infinite chains exist.

Links

• Richard K. Guy, Tanya Khovanova and Julian Salazar, Conway's subprime Fibonacci sequences, arXiv:1207.5099v1 [math.NT]

Crossrefs

Cf. A000045, A020639, A175723, A214551, A014682, A214674, A214892-A214898.

Programs

Mathematica

see A214674