## Signature Sequence

Let be an Irrational Number, define , and let be the sequence obtained by arranging the elements of in increasing order. A sequence is said to be a signature sequence if there Exists a Positive Irrational Number such that , and is called the signature of .

The signature of an Irrational Number is a Fractal Sequence. Also, if is a signature sequence, then the Lower-Trimmed Subsequence is .

References

Kimberling, C. Fractal Sequences and Interspersions.'' Ars Combin. 45, 157-168, 1997.