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A108764
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Products of exactly two supersingular primes (A002267).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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REFERENCES
| Calkin, Neil; Wilf, Herbert (2000), "Recounting the rationals", Amer. Math. Monthly 107 (4): 360-363.
Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.
Conway, J. H. and Norton, S. P. "Monstrous Moonshine." Bull. London Math. Soc. 11, 308-339, 1979.
E. Dijkstra, Selected Writings on Computing, Springer, 1982, p. 232.
Elliott, P. D. T. A. "The multiplicative group of rationals generated by the shifted primes. I." J. Reine Angew. Math. 463 (1995), 169-216.
Elliott, P. D. T. A. "The multiplicative group of rationals generated by the shifted primes. II." J. Reine Angew. Math. 519 (2000), 59-71.
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.
Schinzel, A. and Sierpinski, W. "Sur certaines hypothèses concernant les nombres premiers." Acta Arith. 4, 185-208, 1958. erratum 5 (1958) p. 259.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..120
J. H. Conway, R. K. Guy, W. A. Schneeberger and N. J. A. Sloane, The Primary Pretenders, Acta Arith. 78 (1997), 307-313.
Peter Luschny, The Schinzel-Sierpinski conjecture and the Calkin-Wilf tree.
Eric Weisstein et al., Supersingular Prime.
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FORMULA
| {a(n)} = {p*q: p in A002267 and q in A002267}.
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EXAMPLE
| 1207 = 17 * 71, 3337 = 47 * 71.
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MATHEMATICA
| Union[ Times @@@ Tuples[{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71}, 2]] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 11 2011)
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CROSSREFS
| Cf. A001358, A002267.
Sequence in context: A063762 A001358 A176540 * A193801 A129336 A103607
Adjacent sequences: A108761 A108762 A108763 * A108765 A108766 A108767
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KEYWORD
| easy,fini,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 17 2005
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