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A048578
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Pisot sequence L(3,5).
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5
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3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 8589934593
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OFFSET
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0,1
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COMMENTS
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Lexicographically earliest (when ordered) minimal set of generators for A001969 (numbers with an even number of binary 1's) as a group under A003987(.,.) the XOR operation. - Peter Munn, Aug 21 2019
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REFERENCES
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G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Josef Eschgfäller, Andrea Scarpante, Dichotomic random number generators, arXiv:1603.08500 [math.CO], 2016.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Eric Weisstein's World of Mathematics, Group
Wikipedia, Generating set of a group
Index entries for linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
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a(n) = 2^(n+1)+1.
a(n) = 3*a(n-1) - 2*a(n-2).
O.g.f.: (3-4*x)/(1-3*x+2*x^2). - R. J. Mathar, Nov 23 2007
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MATHEMATICA
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LinearRecurrence[{3, -2}, {3, 5}, 40] (* Harvey P. Dale, Sep 10 2017 *)
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PROG
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(MAGMA) [2^(n+1)+1 : n in [0..40]]; // Vincenzo Librandi, Sep 01 2011
(PARI) x='x+O('x^99); Vec(1/(1-x)+2/(1-2*x)) \\ Altug Alkan, Mar 29 2016
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CROSSREFS
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Subsequence of A000051.
See A008776 for definitions of Pisot sequences.
Cf. A001969, A003987.
Sequence in context: A135728 A083318 A127904 * A087312 A099170 A251705
Adjacent sequences: A048575 A048576 A048577 * A048579 A048580 A048581
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KEYWORD
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nonn,easy
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AUTHOR
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David W. Wilson
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STATUS
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approved
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