A117596 Start with x=6/5; repeatedly apply the map x -> x*ceiling(x); sequence gives numerators of the resulting sequence of fractions.

6, 12, 36, 288, 16704, 55808064, 622908012647232, 77602878444025201997703040704, 1204441348559630271252918141028336694332989128001036771264, 290135792424028156178425357986052529062710984863337179470336908191924417208517059859206222048920739921330978585792

Offset

1,1

Comments

After 18 terms the fractions become integers, the first of which has 57735 digits.

References

N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.

Links

Table of n, a(n) for n=1..10.

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

N. J. A. Sloane, Seven Staggering Sequences.

Example

The sequence of fractions begins 6/5, 12/5, 36/5, 288/5, 16704/5, 55808064/5, 622908012647232/5, 77602878444025201997703040704/5, ... The first 17 denominators are 5, the rest are 1.

Mathematica

f[x_] := x*Ceiling[x]; NestList[f, 6/5, 9] // Numerator (* Jean-François Alcover, Nov 18 2013 *)

Crossrefs

Cf. A072340, A085276.

Sequence in context: A038266 A298881 A256875 * A276601 A096377 A026083

Adjacent sequences: A117593 A117594 A117595 * A117597 A117598 A117599

Keyword

nonn,frac

Author

N. J. A. Sloane, Apr 07 2006

Status

approved