A078466 First cycle is reached under a "Collatz-Fibonacci" transform (cf. comment).

1, 3, 7, 8, 11, 13, 14, 18, 24, 26, 27, 29, 32, 33, 36, 37, 39, 40, 43, 45, 46, 51, 52, 56, 57, 61, 62, 63, 65, 66, 85, 86, 87, 94, 100, 101, 103, 105, 106, 107, 109, 111, 113, 114, 115, 121, 130, 131, 136, 141, 142, 145, 146, 147, 153, 155, 158, 164, 166, 167, 168, 169

Offset

1,2

Comments

Let x(1)=1 x(2)=n; x(k)=x(k-1)+x(k-2) if x(k-1) and x(k-2) have opposite parities; x(k)=abs(x(k-1)-x(k-2))/2 otherwise. Conjecture : for any n x(k) reaches a cycle among 2 cycles : (1;1;0) and (1;2;3;5). Sequence gives values of n such that (1;1;0) is reached.

Links

Table of n, a(n) for n=1..62.

Formula

a(n)/n seems greater than 2 for n large enough and if limit a(n)/n exists, this limit should be > 2.5. Does a(n)/n = O(log(log(n))?

Crossrefs

Sequence in context: A174871 A062863 A194470 * A047528 A069122 A278519

Adjacent sequences: A078463 A078464 A078465 * A078467 A078468 A078469

Keyword

nonn

Author

Benoit Cloitre, Jan 02 2003

Status

approved