A047256 Numbers that are congruent to {0, 1, 2, 3, 5} mod 6.

0, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A047226.

Programs

Mathematica

Flatten[# + {0, 1, 2, 3, 5} & /@ (6 Range[0, 11])] (* or *)
Select[Range[0, 67], MemberQ[{0, 1, 2, 3, 5}, Mod[#, 6]] &] (* Robert G. Wilson v, Sep 26 2016 *)
LinearRecurrence[{1,0,0,0,1,-1},{0,1,2,3,5,6},60] (* Harvey P. Dale, Jul 20 2020 *)

Formula

G.f.: x^2*(1+x)*(x^3 + x^2 + 1) / ( (x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

Sum_{n>=2} (-1)^n/a(n) = (3-2*sqrt(3))*Pi/36 + log(2+sqrt(3))/sqrt(3). - Amiram Eldar, Dec 17 2021

a(n) = n + floor(n/5) - 1. - Aaron J Grech, Oct 03 2024