Number Theory


A Class of Stationary Sequences

Authors: Florentin Smarandache

We define a class of sequences {an} by a1 = a and an+1 = P(an), where P is a polynomial with real coefficients. For which a values, and for which polynomials P will these sequences be constant after a certain rank? Then we generalize it from polynomials P to real functions f. In this note, the author answers this question using as reference F. Lazebnik & Y. Pilipenko's E 3036 problem from A. M. M., Vol. 91, No. 2/1984, p. 140. An interesting property of functions admitting fixed points is obtained.

Comments: 3 pages

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Submission history

[v1] 13 Mar 2010

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