A047263 Numbers that are congruent to {0, 1, 2, 4, 5} mod 6.

0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85

Offset

1,3

Comments

Complement of A016945. - R. J. Mathar, Feb 25 2008

Nonnegative integers m such that floor(2*m^2/12) = 2*floor(m^2/12). See the Crossrefs field of A265187 for similar sequences. - Bruno Berselli, Dec 08 2015

Also, numbers k such that Fibonacci(k) mod 4 = 0, 1 or 3. - Bruno Berselli, Oct 17 2017

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

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

Formula

O.g.f.: x*(x^2+1)*(x^2+x+1)/((x-1)^2*(x^4+x^3+x^2+x+1)). - R. J. Mathar, Feb 25 2008

a(n) = a(n-5) + 6 for n > 5. - R. J. Mathar, Feb 25 2008

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6. - Harvey P. Dale, Oct 05 2014

From Wesley Ivan Hurt, Aug 16 2016: (Start)

a(n) = n + floor((n-4)/5).

a(n) = (6*n - 4 - ((n+1) mod 5))/5.

a(5k) = 6k-1, a(5k-1) = 6k-2, a(5k-2) = 6k-4, a(5k-3) = 6k-5, a(5k-4) = 6k-6. (End)

Sum_{n>=2} (-1)^n/a(n) = log(2+sqrt(3))/sqrt(3) - log(2)/6. - Amiram Eldar, Dec 17 2021

Maple

for n from 0 to 200 do if n mod 6 <> 3 then printf(`%d, `, n) fi: od:
A047263:=n->6*floor(n/5)+[0, 1, 2, 4, 5][(n mod 5)+1]: seq(A047263(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2016

Mathematica

Select[Range[0, 100], Mod[#, 6]!=3&] (* Harvey P. Dale, May 17 2011 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6}, 90] (* Harvey P. Dale, Oct 05 2014 *)

Prog

(Magma) [n : n in [0..100] | n mod 6 in [0, 1, 2, 4, 5]]; // Wesley Ivan Hurt, Aug 16 2016
(PARI) first(n) = {select(x->(x%6!=3), vector(6*n\5, i, i-1))} \\ David A. Corneth, Oct 17 2017

Crossrefs

Cf. A016945, A265187.

Sequence in context: A139143 A183571 A184528 * A039244 A160044 A180917

Adjacent sequences: A047260 A047261 A047262 * A047264 A047265 A047266

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1999

Extensions

More terms from James A. Sellers, Feb 19 2001

Status

approved