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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001622.

Programs

Magma

[n: n in [1..150] | n mod 5 in [2..4]]; // Vincenzo Librandi, Mar 31 2011

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 *)

PARI

a(n)=n\3*5+[-1,2,3][n%3+1] \\ Charles R Greathouse IV, Dec 22 2011

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