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A047304 Numbers not divisible by 7. 10
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A286997 A187396 A020659 * A020658 A195178 A043092
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 14 04:54 EDT 2024. Contains 371655 sequences. (Running on oeis4.)