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A064386
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Numbers of the form 2^n+1 or 4^n-2^n+1.
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1
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1, 2, 3, 5, 9, 13, 17, 33, 57, 65, 129, 241, 257, 513, 993, 1025, 2049, 4033, 4097, 8193, 16257, 16385, 32769, 65281, 65537, 131073, 261633, 262145, 524289, 1047553, 1048577, 2097153, 4192257, 4194305, 8388609, 16773121, 16777217
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Call m exceptional if the binary cyclic code of length 2^k-1 with zeros w and w^m (w primitive in GF(2^k)) is double-error-correcting for infinitely many k. It is conjectured that this sequence (with the initial terms 1 and 2 omitted) gives all odd exceptional m's.
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REFERENCES
| J. F. Dillon, Geometry, codes and difference sets: exceptional connections, in Codes and designs (Columbus, OH, 2000), pp. 73-85, de Gruyter, Berlin, 2002.
H. Janwa, G. McGuire and R. M. Wilson, Double-error-correcting codes and absolutely irreducible polynomials over GF(2), J. Algebra, 178 (1995), 665-676.
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CROSSREFS
| Cf. A064390.
Sequence in context: A098142 A066821 A108568 * A049715 A076095 A085913
Adjacent sequences: A064383 A064384 A064385 * A064387 A064388 A064389
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Sep 28 2001
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