A047471 Numbers that are congruent to {1, 3} mod 8.

1, 3, 9, 11, 17, 19, 25, 27, 33, 35, 41, 43, 49, 51, 57, 59, 65, 67, 73, 75, 81, 83, 89, 91, 97, 99, 105, 107, 113, 115, 121, 123, 129, 131, 137, 139, 145, 147, 153, 155, 161, 163, 169, 171, 177, 179, 185, 187, 193, 195, 201, 203, 209, 211, 217, 219, 225, 227, 233

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			For n=2, a(2) = 8*2-1-12 = 3;
For n=3, a(3) = 8*3-3-12 = 9;
For n=4, a(4) = 8*4-9-12 = 11. - _Vincenzo Librandi_, Aug 06 2010
		

Links

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

Crossrefs

Union of A017077 and A017101.

Cf. A033200 (primes).

Programs

Haskell

a047471 n = a047471_list !! (n-1)
a047471_list = [n | n <- [1..], mod n 8 `elem` [1,3]]
-- Reinhard Zumkeller, Dec 29 2012

Magma

[4*(n-1)-(-1)^n : n in [1..80]]; // Wesley Ivan Hurt, Apr 28 2017

Maple

A047471:=n->4*n - 4 - (-1)^n; seq(A047471(n), n=1..100); # Wesley Ivan Hurt, Jan 30 2014

Mathematica

Table[4 n - 4 - (-1)^n, {n, 100}] (* Wesley Ivan Hurt, Jan 30 2014 *)
#+{1,3}&/@(8*Range[0,30])//Flatten (* or *) LinearRecurrence[{1,1,-1},{1,3,9},60] (* Harvey P. Dale, Jan 05 2017 *)

Formula

G.f.: x*(1+2*x+5*x^2)/((1+x)*(1-x)^2). - Paul Barry, Apr 10 2008

a(n) = 4*(n-1)-(-1)^n. - Rolf Pleisch, Aug 04 2009

a(n) = 8*n-a(n-1)-12, with a(1)=1. - Vincenzo Librandi, Aug 06 2010

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 + sqrt(2)*log(sqrt(2)+1)/4. - Amiram Eldar, Dec 18 2021

Extensions

More terms from Vincenzo Librandi, Aug 06 2010