A047370 Numbers that are congruent to {2, 3, 5} mod 7.

2, 3, 5, 9, 10, 12, 16, 17, 19, 23, 24, 26, 30, 31, 33, 37, 38, 40, 44, 45, 47, 51, 52, 54, 58, 59, 61, 65, 66, 68, 72, 73, 75, 79, 80, 82, 86, 87, 89, 93, 94, 96, 100, 101, 103, 107, 108, 110, 114, 115, 117, 121, 122, 124, 128, 129, 131, 135, 136, 138, 142

Offset

1,1

Comments

Union of A017005, A017017 and A017041. - Michel Marcus, May 25 2014

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

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

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=2, a(2)=3, a(3)=5, a(4)=9. - Harvey P. Dale, Apr 29 2013

a(n) = 7*floor((n-1)/3)+2^((n-1) mod 3)+1. - Gary Detlefs, May 25 2014

a(n) = (1/9)*(21*n+4*sqrt(3)*sin((2*Pi*n)/3)-6*cos((2*Pi*n)/3)-12). - Alexander R. Povolotsky, May 25 2014

a(3k) = 7k-2, a(3k-1) = 7k-4, a(3k-2) = 7k-5. - Wesley Ivan Hurt, Jun 10 2016

Maple

A047370:=n->7*floor((n-1)/3) + 2^((n-1) mod 3)+1; seq(A047370(n), n=1..50); # Wesley Ivan Hurt, May 25 2014

Mathematica

Select[Range[200], MemberQ[{2, 3, 5}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 1, -1}, {2, 3, 5, 9}, 60] (* Harvey P. Dale, Apr 29 2013 *)
Table[7*Floor[(n - 1)/3] + 2^Mod[n - 1, 3] + 1, {n, 50}] (* Wesley Ivan Hurt, May 25 2014 *)

Prog

(Magma) [7*Floor((n-1)/3)+2^((n-1) mod 3)+1: n in [1..50]]; // Wesley Ivan Hurt, May 25 2014
(PARI) x='x + O('x^50); Vec(x*(2+x+2*x^2+2*x^3)/((1+x+x^2)*(x-1)^2)) \\ G. C. Greubel, Feb 21 2017

Crossrefs

Cf. A017005, A017017, A017041.

Sequence in context: A047606 A226826 A333607 * A226820 A072192 A287158

Adjacent sequences: A047367 A047368 A047369 * A047371 A047372 A047373

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1999

Extensions

More terms from Wesley Ivan Hurt, May 25 2014

Status

approved