A214897 Conway's subprime Fibonacci sequence: cycle lengths.

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

Offset

1,2

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

Table of n, a(n) for n=1..7.

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

Mathematica

see A214674

Crossrefs

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

Sequence in context: A112787 A264719 A214792 * A037307 A341820 A296862

Adjacent sequences: A214894 A214895 A214896 * A214898 A214899 A214900

Keyword

nonn

Author

Wouter Meeussen, Jul 29 2012

Status

approved