A162699 Odd numbers not divisible by 7.

1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 75, 79, 81, 83, 85, 87, 89, 93, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 117, 121, 123, 125, 127, 129, 131, 135, 137, 139, 141, 143, 145, 149

Offset: 1

Author

Zak Seidov, Jul 11 2009

Keywords

• nonn
• easy

Comments

Numbers coprime to 14. The asymptotic density of this sequence is 3/7. - Amiram Eldar, Oct 18 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Cf. A045572 (odd numbers not divisible by 5).

Programs

Mathematica

s={}; Do[If[Mod[n, 7] > 0, AppendTo[s, n]], {n, 1, 60, 2}]; s
Table[2 n + 1 + 2*Floor[(2 n - 7)/12], {n, 1, 99}]
DeleteCases[Range[1,151,2],?(Divisible[#,7]&)] (* _Harvey P. Dale, Jul 04 2015 *)

PARI

a(n)=(14*n-7)\12*2+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

a(n) = 2*n + 1 + 2*floor( (2*n-7)/12 ).

a(n) = a(n-1)+a(n-6)-a(n-7). G.f.: x*(x^2+1)*(x^4+2*x^3+x^2+2*x+1)/ ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - R. J. Mathar, Jul 31 2009