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Recently, L. Block has shown that for any mapping      f f       of an interval, whether      f f       has a periodic point whose period contains an odd factor greater than      1 1       depends entirely on the periodic orbits of      f f       whose periods are powers of      2 2      . In this paper the author shows that Block’s result is a special case of a more general phenomenon.

On Block’s condition for simple periodic orbits of functions on an interval