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Numbers that are congruent to {1, 3, 4, 6, 7} mod 8.
1

%I #16 Sep 08 2022 08:44:57

%S 1,3,4,6,7,9,11,12,14,15,17,19,20,22,23,25,27,28,30,31,33,35,36,38,39,

%T 41,43,44,46,47,49,51,52,54,55,57,59,60,62,63,65,67,68,70,71,73,75,76,

%U 78,79,81,83,84,86,87,89,91,92,94,95,97,99,100,102,103,105

%N Numbers that are congruent to {1, 3, 4, 6, 7} mod 8.

%H Vincenzo Librandi, <a href="/A047516/b047516.txt">Table of n, a(n) for n = 1..1000</a>

%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_, May 30 2016: (Start)

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

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

%t Select[Range[140], MemberQ[{1, 3, 4, 6, 7}, Mod[#, 8]] &] (* _Vincenzo Librandi_, May 30 2016 *)

%o (Magma) [n: n in [0..110] | n mod 8 in [1,3,4,6,7]]; // _Vincenzo Librandi_, May 30 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_