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A293481 Numbers with last digit greater than or equal to 5 (in base 10).

%I A293481 #26 Oct 29 2024 14:41:04
%S A293481 5,6,7,8,9,15,16,17,18,19,25,26,27,28,29,35,36,37,38,39,45,46,47,48,
%T A293481 49,55,56,57,58,59,65,66,67,68,69,75,76,77,78,79,85,86,87,88,89,95,96,
%U A293481 97,98,99,105,106,107,108,109,115,116,117,118,119,125,126,127,128,129
%N A293481 Numbers with last digit greater than or equal to 5 (in base 10).
%C A293481 Equivalently, numbers k such that floor(k/5) is odd.
%C A293481 Also numbers k such that ceiling(-k/5) is odd. - _Peter Luschny_, Oct 10 2017
%H A293481 Colin Barker, <a href="/A293481/b293481.txt">Table of n, a(n) for n = 1..500</a>
%H A293481 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A293481 G.f.: x*(5 + x + x^2 + x^3 + x^4 + x^5)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).
%F A293481 a(n) = a(n-1) + a(n-5) - a(n-6).
%F A293481 a(n) = A293292(n) + 5.
%F A293481 a(n) = 2n+3-((n-1) mod 5). - _Chai Wah Wu_, Oct 29 2024
%p A293481 select(n -> type(ceil(-n/5), odd), [$0..130]); # _Peter Luschny_, Oct 10 2017
%t A293481 LinearRecurrence[{1, 0, 0, 0, 1, -1}, {5, 6, 7, 8, 9, 15}, 70]
%t A293481 (* Second program: *)
%t A293481 Select[Range[129], Mod[#, 10] >= 5 &] (* _Jean-François Alcover_, Oct 10 2017 *)
%o A293481 (Magma) [n: n in [0..150] | n mod 10 ge 5];
%o A293481 (PARI) select(k -> (k\5) % 2, vector(130, k, k)) \\ _Peter Luschny_, Oct 10 2017
%o A293481 (PARI) Vec(x*(5 + x + x^2 + x^3 + x^4 + x^5)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^100)) \\ _Colin Barker_, Oct 10 2017
%o A293481 (Python) [k for k in range(130) if (k//5) % 2 == 1] # _Peter Luschny_, Oct 10 2017
%o A293481 (Python)
%o A293481 def A293481(n): return (n<<1)+3-(n-1)%5 # _Chai Wah Wu_, Oct 29 2024
%o A293481 (Sage) [k for k in (0..130) if not 2.divides(k//5)] # _Peter Luschny_, Oct 10 2017
%Y A293481 Complement of A293292.
%Y A293481 Cf. A010122 (first differences, after 3).
%K A293481 nonn,base,easy
%O A293481 1,1
%A A293481 _Bruno Berselli_, Oct 10 2017