The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A091684 a(n) = 0 if n is divisible by 3, otherwise a(n) = n. 6
0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 10, 11, 0, 13, 14, 0, 16, 17, 0, 19, 20, 0, 22, 23, 0, 25, 26, 0, 28, 29, 0, 31, 32, 0, 34, 35, 0, 37, 38, 0, 40, 41, 0, 43, 44, 0, 46, 47, 0, 49, 50, 0, 52, 53, 0, 55, 56, 0, 58, 59, 0, 61, 62, 0, 64, 65, 0, 67, 68, 0, 70, 71, 0, 73, 74, 0, 76, 77, 0, 79, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Multiplicative with a(3^e) = 0, a(p^e) = p^e otherwise. - Mitch Harris, Jun 09 2005
Completely multiplicative with a(3) = 0, a(p) = p otherwise. - Charles R Greathouse IV, Feb 21 2011
LINKS
FORMULA
a(n) = Product_{k=0..2} Sum_{j=1..n} w(3)^(k*j), w(3)=e^(2*Pi*i/3), i=sqrt(-1).
a(n) = 2*n/3 - n*sin(2*Pi*n/3 + Pi/3)/sqrt(3) - n*cos(2*Pi*n/3 + Pi/3)/3.
G.f.: x*(x^4 + 2*x^3 + 2*x + 1)/((x^2 + x + 1)^2*(x - 1)^2). - Ralf Stephan, Jan 29 2004
a(n) = n^3 mod 3n. - Paul Barry, Apr 13 2005
Dirichlet g.f.: zeta(s-1)*(1-1/3^(s-1)). - R. J. Mathar, Feb 10 2011
a(3*n) = 0, a(3*n + 1) = 3*n + 1, a(3*n + 2) = 3*n + 2. a(-n) = -a(n). - Michael Somos, Mar 19 2011
a(n) = n * sign(n mod 3). - Wesley Ivan Hurt, Sep 24 2017
EXAMPLE
x + 2*x^2 + 4*x^4 + 5*x^5 + 7*x^7 + 8*x^8 + 10*x^10 + 11*x^11 + 13*x^13 + ...
MATHEMATICA
f[n_] := If[ Mod[n, 3] == 0, 0, n] (* Or *) n (Fibonacci[n] - 2 Floor[ Fibonacci[n]/2]); Array[f, 78, 0] (* Robert G. Wilson v *)
{#, 0, #}[[Mod[#-1, 3, 1]]]&/@Range[0, 99] (* Federico Provvedi, Jun 15 2021 *)
PROG
(PARI) a(n)=if(n%3, n) \\ Charles R Greathouse IV, Feb 21 2011
(PARI) {a(n) = n * sign( n%3)} /* Michael Somos, Mar 19 2011 */
(Magma) &cat[[0, 3*n+1, 3*n+2]: n in [0..26]]; // Bruno Berselli, Aug 29 2011
CROSSREFS
Sequence in context: A266587 A070692 A162397 * A100050 A164616 A258100
KEYWORD
nonn,mult,easy
AUTHOR
Paul Barry, Jan 28 2004
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 June 15 11:51 EDT 2024. Contains 373407 sequences. (Running on oeis4.)