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A217562 Even numbers not divisible by 5.

%I A217562 #34 Apr 22 2025 02:48:11
%S A217562 2,4,6,8,12,14,16,18,22,24,26,28,32,34,36,38,42,44,46,48,52,54,56,58,
%T A217562 62,64,66,68,72,74,76,78,82,84,86,88,92,94,96,98,102,104,106,108,112,
%U A217562 114,116,118,122,124,126,128,132
%N A217562 Even numbers not divisible by 5.
%C A217562 Numbers ending with 2,4,6,8 in base 10.
%C A217562 No term is divisible by 10 therefore a subsequence of A067251 (Numbers with no trailing zeros in decimal representation).
%C A217562 Union of this sequence with A005408 (The odd numbers) gives A067251.
%C A217562 Union of this sequence with A045572 (Numbers that are odd but not divisible by 5) gives A047201.
%C A217562 The even numbers divisible by 5 are A008592 (Multiples of 10).
%H A217562 Jeremy Gardiner, <a href="/A217562/b217562.txt">Table of n, a(n) for n = 1..4000</a>
%H A217562 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A217562 a(n) = 2*A047201(n).
%F A217562 G.f.: 2*x*(1+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 06 2012
%F A217562 a(n) = 2*(n+floor((n-1)/4)). - _Aaron J Grech_, Sep 28 2024
%F A217562 E.g.f.: (4 - cos(x) + (5*x - 3)*cosh(x) + sin(x) + (5*x - 2)*sinh(x))/2. - _Stefano Spezia_, Sep 28 2024
%t A217562 CoefficientList[Series[2*(1 + x + x^2 + x^3 + x^4)/((1 + x)*(1 + x^2)*(x - 1)^2), {x, 0, 100}], x] (* _Vincenzo Librandi_, Dec 28 2012 *)
%o A217562 (BASIC)
%o A217562 for n=1 to 199
%o A217562 if n mod 5 <> 0 and n mod 2 <> 1 then print str$(n)+", ";
%o A217562 next n
%o A217562 print
%o A217562 (PARI) A217562(n)=(n-1)*5\2+2 \\ _M. F. Hasler_, Oct 07 2012
%o A217562 (Magma) I:=[2, 4, 6, 8, 12]; [n le 5 select I[n] else Self(n-1) + Self(n-4) - Self(n-5): n in [1..60]]; // _Vincenzo Librandi_, Dec 28 2012
%o A217562 (Python)
%o A217562 def A217562(n): return (5*n-1>>1)&-2 # _Chai Wah Wu_, Apr 21 2025
%Y A217562 Cf. A005408, A005843, A045572, A047201, A067251.
%K A217562 nonn,easy
%O A217562 1,1
%A A217562 _Jeremy Gardiner_, Oct 06 2012