A048578 Pisot sequence L(3,5).

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

Offset

0,1

Comments

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

References

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

Links

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).

Formula

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

Mathematica

LinearRecurrence[{3, -2}, {3, 5}, 40] (* Harvey P. Dale, Sep 10 2017 *)

Prog

(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

Crossrefs

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

Keyword

nonn,easy

Author

David W. Wilson

Status

approved