

A004766


Numbers whose binary expansion ends 01.


5



5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225
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OFFSET

1,1


COMMENTS

These are the numbers for which zeta(2*x+1) needs just 3 terms to be evaluated.  Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 16 2004
The binary representation of a(n) has exactly the same number of 0s and 1s as the binary representation of a(n+1).  Gil Broussard, Dec 18 2008
a(n) = number of monomials in nth power of x^4+x^3+x^2+x+1.  Artur Jasinski, Oct 06 2008


LINKS

Table of n, a(n) for n=1..56.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(n) = 8*na(n1)2 (with a(1)=5). [Vincenzo Librandi, Nov 18 2010]
a(n) = 2*a(n1)a(n2). G.f.: x*(x5) / (x1)^2.  Colin Barker, Jun 24 2013


MAPLE

seq( 4*x+1, x=1..100 );


MATHEMATICA

a = {}; k = x^4 + x^3 + x^2 + x + 1; m = k; Do[AppendTo[a, Length[m]]; m = Expand[m*k], {n, 1, 100}]; a (* Artur Jasinski, Oct 06 2008 *)


PROG

(PARI) a(n)=4*n+1 \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Essentially same as A016813.
Sequence in context: A141135 A194395 A162502 * A016813 A198395 A190951
Adjacent sequences: A004763 A004764 A004765 * A004767 A004768 A004769


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



