A047527 Numbers that are congruent to {0, 1, 2, 7} mod 8.

0, 1, 2, 7, 8, 9, 10, 15, 16, 17, 18, 23, 24, 25, 26, 31, 32, 33, 34, 39, 40, 41, 42, 47, 48, 49, 50, 55, 56, 57, 58, 63, 64, 65, 66, 71, 72, 73, 74, 79, 80, 81, 82, 87, 88, 89, 90, 95, 96, 97, 98, 103, 104, 105, 106, 111, 112, 113, 114, 119, 120

Offset

1,3

Comments

Complement of numbers that are congruent to {3, 4, 5, 6} mod 8 (A047425). - Jaroslav Krizek, Dec 19 2009

Links

Table of n, a(n) for n=1..61.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = 3*n-4*floor((n-2)/4)-6+(-1)^n. - Gary Detlefs, Mar 27 2010

G.f.: x^2*(1+x+5*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Harvey P. Dale, Sep 05 2014

From Wesley Ivan Hurt, May 21 2016: (Start)

a(n) = (4n-5+i^(2n)+(1+i)*i^(-n)+(1-i)*i^n)/2 where i = sqrt(-1).

a(2n) = A047522(n), a(2n-1) = A047467(n). (End)

Sum_{n>=2} (-1)^n/a(n) = (5-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4 - Pi/16. - Amiram Eldar, Dec 20 2021

Maple

seq(3*n-4*floor((n-2)/4)-6+(-1)^n, n=1..61); # Gary Detlefs, Mar 27 2010

Mathematica

Select[Range[0, 200], MemberQ[{0, 1, 2, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 7, 8}, 200] (* Harvey P. Dale, Sep 05 2014 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 7]]; // Wesley Ivan Hurt, May 21 2016

Crossrefs

Cf. A103127, A047425, A047467, A047522.

Sequence in context: A093915 A152769 A283565 * A064517 A270804 A167457

Adjacent sequences: A047524 A047525 A047526 * A047528 A047529 A047530

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved