A047304 Numbers not divisible by 7.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66

Offset

1,2

Comments

Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 7. Different from A020658.

More generally the sequence of numbers not divisible by some fixed integer m >= 2 is given by a(n,m) = n - 1 + floor((n+m-2)/(m-1)). - Benoit Cloitre, Jul 11 2009

Complement of A008589. - Reinhard Zumkeller, Nov 30 2009

Links

Ivan Panchenko, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Formula

a(n) = n - 1 + floor((n+5)/6). - Benoit Cloitre, Jul 11 2009

A109720(a(n)) = 1; A082784(a(n)) = 0. - Reinhard Zumkeller, Nov 30 2009

G.f.: x*(1+x+x^2+x^3+x^4+x^5+x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

Sum_{n>=1} (-1)^(n+1)/a(n) = (cot(Pi/7) + tan(Pi/14) - tan(3*Pi/14))*Pi/7. - Amiram Eldar, Dec 31 2021

Mathematica

Select[Table[n, {n, 200}], Mod[#, 7]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)
Drop[Range[70], {7, -1, 7}] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 5, 6, 8}, 60] (* Harvey P. Dale, Aug 01 2021 *)

Prog

(Sage) [i for i in range(67) if gcd(7, i) == 1] # Zerinvary Lajos, Apr 21 2009
(PARI) a(n)=n-1+floor((n+5)/6) \\ Benoit Cloitre, Jul 11 2009

Crossrefs

Cf. A008589, A020658, A082784, A109720.

Sequence in context: A286997 A187396 A020659 * A020658 A195178 A043092

Adjacent sequences: A047301 A047302 A047303 * A047305 A047306 A047307

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved