A047216 Numbers that are congruent to {1, 2} mod 5.

1, 2, 6, 7, 11, 12, 16, 17, 21, 22, 26, 27, 31, 32, 36, 37, 41, 42, 46, 47, 51, 52, 56, 57, 61, 62, 66, 67, 71, 72, 76, 77, 81, 82, 86, 87, 91, 92, 96, 97, 101, 102, 106, 107, 111, 112, 116, 117, 121, 122, 126, 127, 131, 132, 136, 137, 141, 142, 146, 147

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Equivalently, numbers ending in 1, 2, 6 and 7. - Bruno Berselli, Sep 04 2018

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A001622, A047209, A047211, A047212, A176059.

Programs

Magma

[(10*n-3*(-1)^n-9)/4 : n in [1..100]]; // Wesley Ivan Hurt, Dec 29 2016

Maple

A047216:=n->(10*n-3*(-1)^n-9)/4: seq(A047216(n), n=1..100); # Wesley Ivan Hurt, Dec 29 2016

Mathematica

Select[Range[0, 200], MemberQ[{1, 2}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)

PARI

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

Formula

a(n) = 5*n-a(n-1)-7 for n>1, with a(1)=1. - Vincenzo Librandi, Aug 05 2010

G.f.: x*(1+x+3*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Bruno Berselli, Mar 10 2012: (Start)

a(n) = (10*n-3*(-1)^n-9)/4.

a(n) = - A176059(n) + Sum_{i=0..n-1} A176059(i). (End)

From Wesley Ivan Hurt, Dec 29 2016: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.

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

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2*sqrt(5)/5)*Pi/10 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021

E.g.f.: 3 + ((5*x - 9/2)*exp(x) - (3/2)*exp(-x))/2. - David Lovler, Aug 23 2022