A047242 Numbers that are congruent to {0, 1, 3} mod 6.

0, 1, 3, 6, 7, 9, 12, 13, 15, 18, 19, 21, 24, 25, 27, 30, 31, 33, 36, 37, 39, 42, 43, 45, 48, 49, 51, 54, 55, 57, 60, 61, 63, 66, 67, 69, 72, 73, 75, 78, 79, 81, 84, 85, 87, 90, 91, 93, 96, 97, 99, 102, 103, 105, 108, 109, 111, 114, 115, 117, 120, 121, 123

Offset

1,3

Links

Table of n, a(n) for n=1..63.

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

Formula

Equals partial sums of (0, 1, 2, 3, 1, 2, 3, 1, 2, 3, ...). - Gary W. Adamson, Jun 19 2008

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

A214090(a(n)) = 0. - Reinhard Zumkeller, Jul 06 2012

a(n) = a(n-1) + a(n-3) - a(n-4), n>4. - Wesley Ivan Hurt, Dec 03 2014

a(n) = n-1 + floor((n-1)/3) + floor((2n-2)/3). - Wesley Ivan Hurt, Dec 03 2014

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = (6*n-8-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3.

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

a(n) = 2*n - 2 - sign((n-1) mod 3). - Wesley Ivan Hurt, Sep 26 2017

Sum_{n>=2} (-1)^n/a(n) = Pi/12 + log(2)/6 + log(2+sqrt(3))/(2*sqrt(3)). - Amiram Eldar, Dec 14 2021

Maple

A047242:=n->n-1+floor((n-1)/3)+floor((2*n-2)/3): seq(A047242(n), n=1..50); # Wesley Ivan Hurt, Dec 03 2014

Mathematica

Select[Range[0, 200], Mod[#, 6] == 0 || Mod[#, 6] == 1 || Mod[#, 6] == 3 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)

Prog

(Haskell)
a047242 n = a047242_list !! n
a047242_list = elemIndices 0 a214090_list
-- Reinhard Zumkeller, Jul 06 2012
(Magma) [n-1+Floor((n-1)/3)+Floor((2*n-2)/3) : n in [1..50]]; // Wesley Ivan Hurt, Dec 03 2014

Crossrefs

Cf. A047234, A047240, A214090.

Cf. A047261 (complement).

Sequence in context: A289059 A286686 A082847 * A190335 A083951 A284879

Adjacent sequences: A047239 A047240 A047241 * A047243 A047244 A047245

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved