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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A008589, A020658, A082784, A109720.

Programs

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 *)

PARI

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

Sage

[i for i in range(67) if gcd(7,i) == 1] # Zerinvary Lajos, Apr 21 2009

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