OFFSET
1,2
COMMENTS
The asymptotic density of this sequence is 4/7. - Amiram Eldar, Oct 23 2020
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
a(n+12) = a(n) + 21.
a(n) = 21*floor((n-1)/12)+f(n)+floor(f(n)/2)+2^floor(f(n)/4)+floor(((n+5) mod 12)/11)+floor(((n+3) mod 12)/11), where f(n)= (n-1) mod 12. - Gary Detlefs, Sep 22 2013
G.f.: x*(1+x+2*x^2+x^3+3*x^4+2*x^5+x^6+2*x^7+3*x^8+x^9+2*x^10+x^11+x^12) / ( (1+x) *(1+x^2) *(1+x+x^2) *(x^2-x+1) *(x^4-x^2+1) *(x-1)^2 ). - R. J. Mathar, Sep 27 2014
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20, 22}, 67] (* Ray Chandler, Jul 15 2015 *)
Select[Range[100], CoprimeQ[21, #] &] (* Amiram Eldar, Oct 23 2020 *)
PROG
(Sage) [i for i in range(0, 128) if gcd(21, i) == 1]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, May 18 2009
EXTENSIONS
Definition corrected by Leroy Quet, Jun 19 2009
STATUS
approved