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A020515
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4^n - 2^n + 1.
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10
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1, 3, 13, 57, 241, 993, 4033, 16257, 65281, 261633, 1047553, 4192257, 16773121, 67100673, 268419073, 1073709057, 4294901761, 17179738113, 68719214593, 274877382657, 1099510579201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 6th cyclotomic polynomial evaluated at powers of 2.
Referred to as Kasami-Welch numbers by Aubry et al. The first prime values are a(1) = 3, a(2) = 13, a(4) = 241, a(32) = 18446744069414584321, no more for n less than or equal to 100. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 15 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..170
Yves Aubry, Gary Mcguire, Francois Rodier, A few more functions that are not APN infinitely often, Sep 12, 2009. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 15 2009]
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FORMULA
| G.f.: 1/(1-4*x)-1/(1-2*x)+1/(1-x). E.g.f.: e^(4*x)-e^(2*x)+e^x. [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 15 2009]
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MAPLE
| with(numtheory, cyclotomic):seq(cyclotomic(6, 2**i), i=0..24);
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PROG
| (MAGMA) [4^n - 2^n + 1: n in [0..40]]; // Vincenzo Librandi, Apr 25 2011
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CROSSREFS
| Sequence in context: A095934 A151220 A151221 * A049086 A010921 A163606
Adjacent sequences: A020512 A020513 A020514 * A020516 A020517 A020518
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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