s-Additive Sequence

A generalization of an Ulam Sequence in which each term is the Sum of two earlier terms in exactly $s$ ways. $(s,t)$-additive sequences are a further generalization in which each term has exactly $s$ representations as the Sum of $t$ distinct earlier numbers. It is conjectured that 0-additive sequences ultimately have periodic differences of consecutive terms (Guy 1994, p. 233).

See also Greedy Algorithm, Stöhr Sequence, Ulam Sequence

References

Finch, S. R. ``Conjectures about $s$-Additive Sequences.'' Fib. Quart. 29, 209-214, 1991.

Finch, S. R. ``Are 0-Additive Sequences Always Regular?'' Amer. Math. Monthly 99, 671-673, 1992.

Finch, S. R. ``On the Regularity of Certain 1-Additive Sequences.'' J. Combin. Th. Ser. A. 60, 123-130, 1992.

Finch, S. R. ``Patterns in 1-Additive Sequences.'' Experiment. Math. 1, 57-63, 1992.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 110 and 233, 1994.

Ulam, S. M. Problems in Modern Mathematics. New York: Interscience, p. ix, 1964.