A047201 Numbers not divisible by 5.
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
Offset: 1
Links
- 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).
Programs
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Haskell
a047201 n = a047201_list !! (n-1) a047201_list = [x | x <- [1..], mod x 5 > 0] -- Reinhard Zumkeller, Dec 17 2011
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Magma
[Floor((15*n-1)/12): n in [1..70]]; // Vincenzo Librandi, Apr 06 2015
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Maple
seq(floor((15*n-1)/12), n=1..56); # Gary Detlefs, Mar 07 2010
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Mathematica
Select[Table[n,{n,200}],Mod[#,5]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *) -
PARI
a(n)= n+(n-1)\4 \\ corrected by Michel Marcus, Sep 02 2022
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PARI
a(n)=n-1+floor((n+3)/4) \\ Benoit Cloitre, Jul 11 2009
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Python
def A047201(n): return n+(n-1>>2) # Chai Wah Wu, Feb 24 2025
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Sage
[i for i in range(72) if gcd(5,i) == 1] # Zerinvary Lajos, Apr 21 2009
Formula
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
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
Extensions
Comment from Lekraj Beedassy, Dec 17 2006 is now the current name. - Wesley Ivan Hurt, Jun 25 2015
Comments