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A047201
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Numbers not divisible by 5.
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48
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1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87
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OFFSET
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1,2
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COMMENTS
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Original name was: Numbers that are congruent to {1, 2, 3, 4} mod 5.
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 A008587. - Reinhard Zumkeller, Nov 30 2009
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
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G.f.: (x+2*x^2+3*x^3+4*x^4+4*x^5+3*x^6+2*x^7+x^8)/(1-x^4)^2 (not reduced). - Len Smiley
a(n) = 5+a(n-4).
G.f.: x*(1+x+x^2+x^3+x^4)/((1-x)*(1-x^4)).
a(n) = n-1+floor((n+3)/4). - Benoit Cloitre, Jul 11 2009
A011558(a(n))=1; A079998(a(n))=0. - Reinhard Zumkeller, Nov 30 2009
a(n) = floor((15*n-1)/12). - Gary Detlefs, Mar 07 2010
a(n) = A225496(n) for n <= 42. - Reinhard Zumkeller, May 09 2013
From Wesley Ivan Hurt, Jun 22 2015: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5), n>5.
a(n) = (10*n-5-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))/8. (End)
E.g.f.: 1 + (1/4)*(-cos(x) + (-3 + 5*x)*cosh(x) + sin(x) + (-2 + 5*x)*sinh(x)). - Stefano Spezia, Dec 01 2019
a(n) = floor((5*n-1)/4). - Wolfdieter Lang, Sep 30 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2/sqrt(5))*Pi/5 = A179290 * A019692 / 10. - Amiram Eldar, Dec 07 2021
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MAPLE
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seq(floor((15*n-1)/12), n=1..56); # Gary Detlefs, Mar 07 2010
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MATHEMATICA
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Select[Table[n, {n, 200}], Mod[#, 5]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)
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PROG
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(PARI) a(n)= n+(n-1)\4 \\ corrected by Michel Marcus, Sep 02 2022
(PARI) a(n)=n-1+floor((n+3)/4) \\ Benoit Cloitre, Jul 11 2009
(Sage) [i for i in range(72) if gcd(5, i) == 1] # Zerinvary Lajos, Apr 21 2009
(Haskell)
a047201 n = a047201_list !! (n-1)
a047201_list = [x | x <- [1..], mod x 5 > 0]
-- Reinhard Zumkeller, Dec 17 2011
(Magma) [Floor((15*n-1)/12): n in [1..70]]; // Vincenzo Librandi, Apr 06 2015
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CROSSREFS
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Cf. A019692, A045572, A179290.
Sequence in context: A358849 A039116 A330002 * A225496 A261189 A023721
Adjacent sequences: A047198 A047199 A047200 * A047202 A047203 A047204
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Comment from Lekraj Beedassy, Dec 17 2006 is now the current name. - Wesley Ivan Hurt, Jun 25 2015
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STATUS
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approved
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