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

1,2

Comments

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

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).

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

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

Maple

seq(floor((15*n-1)/12), n=1..56); # Gary Detlefs, Mar 07 2010

Mathematica

Select[Table[n, {n, 200}], Mod[#, 5]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)

Prog

(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

Crossrefs

Cf. A019692, A045572, A179290.

Sequence in context: A358849 A039116 A330002 * A225496 A261189 A023721

Adjacent sequences: A047198 A047199 A047200 * A047202 A047203 A047204

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Comment from Lekraj Beedassy, Dec 17 2006 is now the current name. - Wesley Ivan Hurt, Jun 25 2015

Status

approved