A047202 Numbers that are congruent to {2, 3, 4} mod 5.

2, 3, 4, 7, 8, 9, 12, 13, 14, 17, 18, 19, 22, 23, 24, 27, 28, 29, 32, 33, 34, 37, 38, 39, 42, 43, 44, 47, 48, 49, 52, 53, 54, 57, 58, 59, 62, 63, 64, 67, 68, 69, 72, 73, 74, 77, 78, 79, 82, 83, 84, 87, 88, 89, 92, 93, 94, 97, 98, 99, 102, 103, 104, 107, 108

Offset

1,1

Links

Stefano Spezia, Table of n, a(n) for n = 1..10000

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

Formula

G.f.: x*(2+x+x^2+x^3) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 07 2011

From Wesley Ivan Hurt, Jun 14 2016: (Start)

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

a(n) = (15*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.

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

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

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((5+sqrt(5))/10)*Pi/5 + log(phi)/sqrt(5) - 3*log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 16 2023

Maple

A047202:=n->(15*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047202(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

Mathematica

Select[Range[0, 200], MemberQ[{2, 3, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)

Prog

(Magma) [n: n in [1..150] | n mod 5 in [2..4]]; // Vincenzo Librandi, Mar 31 2011
(PARI) a(n)=n\3*5+[-1, 2, 3][n%3+1] \\ Charles R Greathouse IV, Dec 22 2011

Crossrefs

Cf. A001622.

Sequence in context: A061856 A105941 A276876 * A064953 A097503 A030701

Adjacent sequences: A047199 A047200 A047201 * A047203 A047204 A047205

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved