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

1,1

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.

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.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A001358, A002267.

Sequence in context: A240938 A001358 A176540 * A193801 A129336 A226526

Adjacent sequences: A108761 A108762 A108763 * A108765 A108766 A108767

Keyword

easy,fini,full,nonn

Author

Jonathan Vos Post, Jun 17 2005

Status

approved