login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048578 Pisot sequence L(3,5). 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 (list; graph; refs; listen; history; text; internal format)
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
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
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.
Sequence in context: A135728 A083318 A127904 * A087312 A099170 A251705
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 08:12 EST 2023. Contains 367515 sequences. (Running on oeis4.)