Størmer Number

A Størmer number is a positive integer n for which the greatest prime factor p of n^2+1 is at least 2n. Every Gregory number t_x can be expressed uniquely as a sum of t_ns where the ns are Størmer numbers. The first few Størmer numbers are given by Conway and Guy (1996) and Todd (1949) and are given by n=1, 2, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 19, 20, ... (OEIS A005528), corresponding to greatest prime factors 2, 5, 17, 13, 37, 41, 101, 61, 29, ... (OEIS A005529).

See also

Greatest Prime Factor, Gregory Number, Inverse Tangent

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Conway, J. H. and Guy, R. K. "Størmer's Numbers." The Book of Numbers. New York: Springer-Verlag, pp. 245-248, 1996.Sloane, N. J. A. Sequences A005528/M0950 and A005529/M1505 in "The On-Line Encyclopedia of Integer Sequences."Todd, J. "A Problem on Arc Tangent Relations." Amer. Math. Monthly 56, 517-528, 1949.

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Størmer Number

Cite this as:

Weisstein, Eric W. "Størmer Number." From MathWorld--A Wolfram Web Resource.

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