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Størmer Number

A Størmer number is a Positive Integer $n$ for which the largest Prime factor $p$ of $n^2+1$ is at least $2n$. Every Gregory Number $t_x$ can be expressed uniquely as a sum of $t_n$s where the $n$s are Størmer numbers. Conway and Guy (1996) give a table of Størmer numbers reproduced below (Sloane's A005529). In a paper on Inverse Tangent relations, Todd (1949) gives a similar compilation.

$n$ $p$ $n$ $p$ $n$ $p$ $n$ $p$ $n$ $p$
1 2 10 101 19 181 26 677 35 613
2 5 11 61 20 401 27 73 36 1297
4 17 12 29 22 97 28 157 37 137
5 13 14 197 23 53 29 421 39 761
6 37 15 113 24 577 33 109 40 1601
9 41 16 257 25 313 34 89 42 353

See also Gregory Number, Inverse Tangent


References

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. Sequence A005529/M1505 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

Todd, J. ``A Problem on Arc Tangent Relations.'' Amer. Math. Monthly 56, 517-528, 1949.




© 1996-9 Eric W. Weisstein
1999-05-26