A047476 Numbers that are congruent to {0, 1, 2, 3} mod 8.

0, 1, 2, 3, 8, 9, 10, 11, 16, 17, 18, 19, 24, 25, 26, 27, 32, 33, 34, 35, 40, 41, 42, 43, 48, 49, 50, 51, 56, 57, 58, 59, 64, 65, 66, 67, 72, 73, 74, 75, 80, 81, 82, 83, 88, 89, 90, 91, 96, 97, 98, 99, 104, 105, 106, 107, 112, 113, 114, 115, 120, 121, 122

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Primes of this sequence are in A033203. All of these numbers satisfy the condition that n XOR 4 = n + 4. - Brad Clardy, Jul 24 2012

Numbers k such that floor(k/4) = 2*floor(k/8). - Bruno Berselli, Oct 05 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A033203 (primes), A047467, A047471.

Programs

Haskell

a047476 n = a047476_list !! (n-1)
a047476_list = [n | n <- [1..], mod n 8 <= 3]
-- Reinhard Zumkeller, Dec 29 2012

Magma

I:=[0, 1, 2, 3, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 16 2012

Maple

A047476:=n->(-7-(-1)^n-(1-I)*(-I)^n-(1+I)*I^n+4*n)/2: seq(A047476(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Select[Range[0,300], MemberQ[{0,1,2,3}, Mod[#,8]]&] (* Vincenzo Librandi, May 16 2012 *)
LinearRecurrence[{1,0,0,1,-1},{0,1,2,3,8},100] (* G. C. Greubel, Jun 01 2016 *)

PARI

x='x+O('x^100); concat(0, Vec(x^2*(1+x+x^2+5*x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015

Formula

a(n) = 8 * floor(n/4) + (n mod 4), with offset 0.. a(0)=0. - Gary Detlefs, Mar 09 2010

From Colin Barker, May 14 2012: (Start)

a(n) = (-7 - (-1)^n - (1-i)*(-i)^n - (1+i)*i^n + 4*n)/2, where i=sqrt(-1).

G.f.: x^2*(1 + x + x^2 + 5*x^3)/((1 - x)^2*(1 + x)*(1 + x^2)). (End)

a(n) = a(n-1) + a(n-4) - a(n-5). - Vincenzo Librandi, May 16 2012

a(2*k) = A047471, a(2*k-1) = A047467(k). - Wesley Ivan Hurt, Jun 01 2016

E.g.f.: 5 + sin(x) - cos(x) + (2*x - 3)*sinh(x) + 2*(x - 2)*cosh(x). - Ilya Gutkovskiy, Jun 01 2016

Sum_{n>=2} (-1)^n/a(n) = (2*sqrt(2)-1)*Pi/16 + 5*log(2)/8. - Amiram Eldar, Dec 19 2021