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

1,2

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A309135 A088607 A296243 * A325129 A368603 A173263

Adjacent sequences: A162696 A162697 A162698 * A162700 A162701 A162702

Keyword

nonn,easy

Author

Zak Seidov, Jul 11 2009

Status

approved