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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A097325, A122841.

Programs

Haskell

a047253 n = n + n `div` 5
a047253_list = [1..5] ++ map (+ 6) a047253_list
-- Reinhard Zumkeller, Nov 10 2013

Mathematica

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

PARI

a(n)= 1+n+n\5

PARI

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

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

Extensions

Extended by R. J. Mathar, Oct 18 2008