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Search: id:A103204
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| A103204 |
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a(1) = 2; a(2) = 4; a(n) = 2*a(n-1) - 1. |
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+0
3
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| 2, 4, 7, 13, 25, 49, 97, 193, 385, 769, 1537, 3073, 6145, 12289, 24577, 49153, 98305, 196609, 393217, 786433, 1572865, 3145729, 6291457, 12582913, 25165825, 50331649, 100663297, 201326593, 402653185, 805306369, 1610612737, 3221225473
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A sequence of Galois Fields from a study of {and, xor} logical information.
GF[2] is taken as a Boolean algebra start. GF[2]->GF[4]->GF[7]->GF[13]->GF[25]->GF[49]-> GF[97]->GF[193] as Category theory parallel to the Lie group sequence: U(1)->SU(2)->SU(3)->SU(4)->SU(5)->SU(7)->SU(10)->SU(14) After the 8th field there is a category symmetry breaking that isolates a supersymmetry.
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FORMULA
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3*2^(n-1) + 1. - Ralf Stephan, May 18 2007
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MATHEMATICA
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a[1] = 2; a[2] = 4; a[n_] := a[n] = 2*a[n - 1] - 1; Table[a[n], {n, 1, 32}]
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CROSSREFS
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Cf. A003945(n-1) + 1.
Sequence in context: A082423 A119266 A102026 this_sequence A017995 A099155 A068031
Adjacent sequences: A103201 A103202 A103203 this_sequence A103205 A103206 A103207
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 19 2005
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