A047550 Numbers that are congruent to {5, 7} mod 8.

5, 7, 13, 15, 21, 23, 29, 31, 37, 39, 45, 47, 53, 55, 61, 63, 69, 71, 77, 79, 85, 87, 93, 95, 101, 103, 109, 111, 117, 119, 125, 127, 133, 135, 141, 143, 149, 151, 157, 159, 165, 167, 173, 175, 181, 183, 189, 191, 197, 199, 205, 207, 213, 215, 221, 223, 229, 231, 237, 239, 245, 247, 253, 255, 261

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Union of A004770 and A004771.

Programs

Maple

A047550:=n->4*n-(-1)^n; seq(A047550(n), n=1..100); # Wesley Ivan Hurt, Mar 31 2014

Mathematica

With[{r8=8*Range[0,40]},Sort[Join[r8+5,r8+7]]] (* or *) LinearRecurrence[ {1,1,-1},{5,7,13},80] (* Harvey P. Dale, Jun 04 2012 *)
Table[4 n - (-1)^n, {n, 100}] (* Wesley Ivan Hurt, Mar 31 2014 *)

PARI

Vec(x*(5+2*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Colin Barker, Aug 26 2016

Formula

a(n) = 8*n-a(n-1)-4 (with a(1)=5). - Vincenzo Librandi, Aug 06 2010

a(n) = 4*n-(-1)^n. - Rolf Pleisch, Nov 02 2010

a(1)=5, a(2)=7, a(3)=13; for n>3, a(n) = a(n-1)+a(n-2)-a(n-3). - Harvey P. Dale, Jun 04 2012

G.f.: x*(5+2*x+x^2) / ((1-x)^2*(1+x)). - Colin Barker, Aug 26 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 - sqrt(2)*log(sqrt(2)+1)/4. - Amiram Eldar, Dec 19 2021

E.g.f.: 1 + 4*x*exp(x) - exp(-x). - David Lovler, Sep 02 2022

Extensions

More terms from Vincenzo Librandi, Aug 06 2010