A047245 Numbers that are congruent to {1, 2, 3} mod 6.

1, 2, 3, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 37, 38, 39, 43, 44, 45, 49, 50, 51, 55, 56, 57, 61, 62, 63, 67, 68, 69, 73, 74, 75, 79, 80, 81, 85, 86, 87, 91, 92, 93, 97, 98, 99, 103, 104, 105, 109, 110, 111, 115, 116, 117, 121, 122, 123

Offset

1,2

Comments

a(k)^m is a term iff {a(k) is odd and m is a nonnegative integer} or {m is in A004273}. - Jerzy R Borysowicz, May 08 2023

Links

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

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

Formula

From Johannes W. Meijer, Jun 07 2011: (Start)

a(n) = ceiling(n/3) + ceiling((n-1)/3) + ceiling((n-2)/3) + 3*ceiling((n-3)/3).

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

a(n) = 3*floor((n-1)/3) + n. - Gary Detlefs, Dec 22 2011

From Wesley Ivan Hurt, Apr 13 2015: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = 2*n-3 + ((2*n-3) mod 3). (End)

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

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

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

Sum_{n>=1} (-1)^(n+1)/a(n) = (9-2*sqrt(3))*Pi/36 + log(2+sqrt(3))/(2*sqrt(3)) - log(2)/6. - Amiram Eldar, Dec 14 2021

Maple

A047245:=n->2*n-3+((2*n-3) mod 3): seq(A047245(n), n=1..100); # Wesley Ivan Hurt, Apr 13 2015

Mathematica

Select[Range[0, 200], Mod[#, 6] == 1 || Mod[#, 6] == 2 || Mod[#, 6] == 3 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
Flatten[Table[{6n + 1, 6n + 2, 6n + 3}, {n, 0, 19}]] (* Alonso del Arte, Jul 07 2011 *)
Select[Range[0, 200], MemberQ[{1, 2, 3}, Mod[#, 6]] &] (* Vincenzo Librandi, Apr 14 2015 *)

Prog

(Magma) [2*n-3+((2*n-3) mod 3) : n in [1..100]]; // Wesley Ivan Hurt, Apr 13 2015
(PARI) a(n) = 3*floor((n-1)/3) + n; \\ David Lovler, Aug 03 2022

Crossrefs

Cf. A047240, A047244, A047258 (complement).

Sequence in context: A327224 A231624 A194381 * A070752 A039582 A026310

Adjacent sequences: A047242 A047243 A047244 * A047246 A047247 A047248

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved