A047513 Numbers that are congruent to {0, 1, 2, 4, 6, 7} mod 8.

0, 1, 2, 4, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 70, 71, 72, 73, 74, 76, 78, 79, 80, 81, 82, 84, 86, 87, 88

Offset

1,3

Comments

The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4, etc. - Bruno Berselli, Nov 28 2012

Nonnegative m such that floor(k*(m/4)^2) = k*floor((m/4)^2), where k = 2 or 3. - Bruno Berselli, Dec 03 2015

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Formula

From Chai Wah Wu, May 29 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6), n>6.

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

From Wesley Ivan Hurt, Jun 15 2016: (Start)

a(n) = (24*n-24-2*sqrt(3)*(cos((1-4*n)*Pi/6)-3*cos((2*n+1)*Pi/6)))/18.

a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-4, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)

Sum_{n>=2} (-1)^n/a(n) = (4-sqrt(2))*log(2)/8 + sqrt(2)*log(sqrt(2)+2)/4. - Amiram Eldar, Dec 27 2021

Maple

A047513:=n->(24*n-24-2*sqrt(3)*(cos((1-4*n)*Pi/6)-3*cos((2*n+1)*Pi/6)))/18: seq(A047513(n), n=1..100); # Wesley Ivan Hurt, Jun 15 2016

Mathematica

Select[Range[0, 75], Function[k, Mod[#, 8] == k] /@ Nor[3, 5] &] (* or *) Select[Range[0, 75], Function[k, Floor[k (#/4)^2] == k Floor[(#/4)^2]] /@ Or[2, 3] &] (* Michael De Vlieger, Dec 03 2015 *)
Select[Range[0, 100], MemberQ[{0, 1, 2, 4, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Apr 26 2016 *)
LinearRecurrence[{2, -2, 2, -2, 2, -1}, {0, 1, 2, 4, 6, 7}, 50] (* G. C. Greubel, May 29 2016 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 4, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A047498, A047581.

Sequence in context: A153351 A153343 A136499 * A039068 A260399 A229785

Adjacent sequences: A047510 A047511 A047512 * A047514 A047515 A047516

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved