A108764 Products of exactly two supersingular primes (A002267).

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 77, 82, 85, 87, 91, 93, 94, 95, 115, 118, 119, 121, 123, 133, 141, 142, 143, 145, 155, 161, 169, 177, 187, 203, 205, 209, 213, 217, 221, 235, 247, 253, 287, 289, 295, 299

Offset: 1

Author

Jonathan Vos Post, Jun 17 2005

Keywords

• easy
• fini
• full
• nonn

Comments

There are exactly 15 supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59 and 71 (A002267). The supersingular primes are exactly the set of primes that divide the group order of the Monster group.

Peter Luschny's link shows how this sequence may be connected to Schinzel-Sierpinski conjecture and the Calkin-Wilf tree.

Examples

			1207 = 17 * 71, 3337 = 47 * 71.
		

References

• E. Dijkstra, Selected Writings on Computing, Springer, 1982, p. 232.
• Ogg, A. P. "Modular Functions." In The Santa Cruz Conference on Finite Groups. Held at the University of California, Santa Cruz, Calif., 1979 (Ed. B. Cooperstein and G. Mason). Providence, RI: Amer. Math. Soc., pp. 521-532, 1980.
• Silverman, J. H. The Arithmetic of Elliptic Curves II. New York: Springer-Verlag, 1994.

Links

• T. D. Noe, Table of n, a(n) for n = 1..120
• N. Calkin and H. S. Wilf, Recounting the rationals, Amer. Math. Monthly, 107 (No. 4, 2000), pp. 360-363.
• Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.
• J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
• J. H. Conway, R. K. Guy, W. A. Schneeberger and N. J. A. Sloane, The Primary Pretenders, Acta Arith. 78 (1997), 307-313.
• P. D. T. A. Elliott, The multiplicative group of rationals generated by the shifted primes. I., J. Reine Angew. Math. 463 (1995), 169-216.
• P. D. T. A. Elliott, The multiplicative group of rationals generated by the shifted primes. II. J. Reine Angew. Math. 519 (2000), 59-71.
• Peter Luschny, The Schinzel-Sierpinski conjecture and the Calkin-Wilf tree.
• A. Schinzel and W. Sierpinski, Sur certaines hypotheses concernant les nombres premiers, Acta Arithmetica 4 (1958), 185-208; erratum 5 (1958) p. 259.
• Eric Weisstein et al., Supersingular Prime.

Crossrefs

Cf. A001358, A002267.

Programs

Mathematica

Union[ Times @@@ Tuples[{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71}, 2]] (*Robert G. Wilson v, Feb 11 2011 *)

Formula

{a(n)} = {p*q: p in A002267 and q in A002267}.