A085785 Start at (2n+1)/4 and iterate the map x -> x*ceiling(x); sequence gives number of steps for denominator to drop to 1 or 2; or -1 if this never happens.

1, 1, 3, 7, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 6, 3, 1, 1, 4, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 5, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 3, 5, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 6, 7, 1, 1, 3, 5, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 5, 3, 1, 1, 5, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 8, 3, 1, 1, 2, 2, 1

Offset

2,3

Comments

We conjecture that the denominator always does drop.

Links

Table of n, a(n) for n=2..106.

J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Crossrefs

A073341 gives number of steps until reach an integer. Cf. A085817, A085833.

Sequence in context: A335918 A048292 A072450 * A200235 A127929 A228147

Adjacent sequences: A085782 A085783 A085784 * A085786 A085787 A085788

Keyword

nonn

Author

N. J. A. Sloane, Aug 16 2003

Status

approved