A160545 Numbers coprime to 21.

1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 26, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 50, 52, 53, 55, 58, 59, 61, 62, 64, 65, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 85, 86, 88, 89, 92, 94, 95, 97, 100, 101, 103, 104, 106, 107, 109, 110, 113, 115, 116

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

Cf. A162699, A045572.

Sequence in context: A026174 A120685 A284472 * A161790 A131396 A131391

Adjacent sequences: A160542 A160543 A160544 * A160546 A160547 A160548

Keyword

nonn,easy

Author

Zerinvary Lajos, May 18 2009

Extensions

Definition corrected by Leroy Quet, Jun 19 2009

Status

approved