A047253 Numbers that are congruent to {1, 2, 3, 4, 5} mod 6.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 86

Offset

1,2

Comments

Numbers that are not divisible by 6. - Benoit Cloitre, Jul 11 2009

More generally the sequence a(n,m) 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

Links

Ivan Panchenko, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

a(n) = 5 + a(n-5).

G.f.: x*(1+x)*(1+x+x^2)*(x^2-x+1) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ).

a(n) = n - 1 + floor((n+4)/5). - Benoit Cloitre, Jul 11 2009

A122841(a(n)) = 0. - Reinhard Zumkeller, Nov 10 2013

Sum_{n>=1} (-1)^(n+1)/a(n) = (15-4*sqrt(3))*Pi/36. - Amiram Eldar, Dec 31 2021

Mathematica

Select[Table[n, {n, 200}], Mod[#, 6]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011*)

Prog

(PARI) a(n)= 1+n+n\5
(PARI) a(n)=n-1+floor((n+4)/5) \\ Benoit Cloitre, Jul 11 2009
(Haskell)
a047253 n = n + n `div` 5
a047253_list = [1..5] ++ map (+ 6) a047253_list
-- Reinhard Zumkeller, Nov 10 2013

Crossrefs

Cf. A097325, A122841.

Sequence in context: A194386 A187390 A039215 * A248910 A254278 A204878

Adjacent sequences: A047250 A047251 A047252 * A047254 A047255 A047256

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Extended by R. J. Mathar, Oct 18 2008

Status

approved