A047339 Numbers that are congruent to {2, 3, 4} mod 7.

2, 3, 4, 9, 10, 11, 16, 17, 18, 23, 24, 25, 30, 31, 32, 37, 38, 39, 44, 45, 46, 51, 52, 53, 58, 59, 60, 65, 66, 67, 72, 73, 74, 79, 80, 81, 86, 87, 88, 93, 94, 95, 100, 101, 102, 107, 108, 109, 114, 115, 116, 121, 122, 123, 128, 129, 130, 135, 136, 137, 142

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

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

Formula

a(n+1) = 7*floor(n/3)+(n mod 3)+2. - Gary Detlefs, Mar 09 2010

G.f.: x*(2+x+x^2+3*x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 08 2016: (Start)

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

a(n) = (21*n-15-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-3, a(3k-1) = 7k-4, a(3k-2) = 7k-5. (End)

Maple

seq(7*floor(n/3)+(n mod 3)+2, n= 0..52); # Gary Detlefs, Mar 09 2010

Mathematica

Select[Range[0, 150], MemberQ[{2, 3, 4}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 08 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [2..4]]; // Wesley Ivan Hurt, Jun 08 2016

Crossrefs

Sequence in context: A165315 A284681 A309346 * A250483 A294485 A332772

Adjacent sequences: A047336 A047337 A047338 * A047340 A047341 A047342

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved