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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved