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

Author

Zerinvary Lajos, May 18 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A162699, A045572.

Programs

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 *)

Sage

[i for i in range(0,128) if gcd(21, i) == 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

Extensions

Definition corrected by Leroy Quet, Jun 19 2009