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.