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A047577 Numbers that are congruent to {0, 1, 5, 6, 7} mod 8. 1

%I

%S 0,1,5,6,7,8,9,13,14,15,16,17,21,22,23,24,25,29,30,31,32,33,37,38,39,

%T 40,41,45,46,47,48,49,53,54,55,56,57,61,62,63,64,65,69,70,71,72,73,77,

%U 78,79,80,81,85,86,87,88,89,93,94,95,96,97,101,102,103

%N Numbers that are congruent to {0, 1, 5, 6, 7} mod 8.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F From _Chai Wah Wu_, Jun 10 2016: (Start)

%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

%F G.f.: x^2*(x^4 + x^3 + x^2 + 4*x + 1)/(x^6 - x^5 - x + 1). (End)

%F From _Wesley Ivan Hurt_, Jul 27 2016: (Start)

%F a(n) = a(n-5) + 8 for n>5.

%F a(n) = (40*n - 25 + 3*(n mod 5) + 3*((n+1) mod 5) - 12*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25.

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

%p A047577:=n->8*floor(n/5)+[0, 1, 5, 6, 7][(n mod 5)+1]: seq(A047577(n), n=0..100); # _Wesley Ivan Hurt_, Jul 27 2016

%t Select[Range[0, 100], MemberQ[{0, 1, 5, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 27 2016 *)

%o (MAGMA) [n : n in [0..150] | n mod 8 in [0, 1, 5, 6, 7]]; // _Wesley Ivan Hurt_, Jul 27 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)