Journal of Integer Sequences, Vol. 20 (2017), Article 17.8.8

Aperiodic Compositions and Classical Integer Sequences

Margherita Maria Ferrari and Norma Zagaglia Salvi
Department of Mathematics
Politecnico di Milano
Milano, 20133


In this paper we define the notion of singular composition of a positive integer. We provide a characterization of these compositions, together with methods for decomposing and also extending a singular composition in terms of other singular compositions. Consecutive extensions of particular compositions determine sequences of integers which coincide with classical integer sequences involving Fibonacci and Lucas numbers.

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(Concerned with sequences A000032 A000045 A001075 A001519 A002310 A005248.)

Received April 20 2017; revised versions received May 11 2017; August 2 2017. Published in Journal of Integer Sequences, September 5 2017.

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