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Stöhr Sequence

A Stöhr sequence for a fixed integer h>=2 starts with a_1=1. For n>=1, a_(n+1) is the least integer greater than a_n which cannot be written as the sum of at most h distinct addends among the terms a_1, a_2, ..., a_n. This defines the h-Stöhr sequence. The first few of these are given in the following table.

hOEISh-Stöhr sequence
2A0336271, 2, 4, 7, 10, 13, 16, 19, 22, 25, ...
3A0264741, 2, 4, 8, 15, 22, 29, 36, 43, 50, ...
4A0510391, 2, 4, 8, 16, 31, 46, 61, 76, 91, ...
5A0510401, 2, 4, 8, 16, 32, 63, 94, 125, 156, ...

See also

Greedy Algorithm, Integer Relation, Postage Stamp Problem, s-Additive Sequence, Subset Sum Problem, Sum-Free Set, Ulam Sequence

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References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 233, 1994.Mossige, S. "The Postage Stamp Problem: An Algorithm to Determine the h-Range on the h-Range Formula on the Extremal Basis Problem for k=4." Math. Comput. 69, 325-337, 2000.Selmer, E. S. "On Stöhr's Recurrent h-Bases for N." Kgl. Norske Vid. Selsk. Skrifter 3, 1-15, 1986.Selmer, E. S. and Mossige, S. "Stöhr Sequences in the Postage Stamp Problem." Bergen Univ. Dept. Pure Math., No. 32, Dec. 1984.Sloane, N. J. A. Sequences A026474, A033627, A051039, and A051040 in "The On-Line Encyclopedia of Integer Sequences."

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Stöhr Sequence

Cite this as:

Weisstein, Eric W. "Stöhr Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StoehrSequence.html

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