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A217562
Even numbers not divisible by 5.
4
2, 4, 6, 8, 12, 14, 16, 18, 22, 24, 26, 28, 32, 34, 36, 38, 42, 44, 46, 48, 52, 54, 56, 58, 62, 64, 66, 68, 72, 74, 76, 78, 82, 84, 86, 88, 92, 94, 96, 98, 102, 104, 106, 108, 112, 114, 116, 118, 122, 124, 126, 128, 132
OFFSET
1,1
COMMENTS
Numbers ending with 2,4,6,8 in base 10.
No term is divisible by 10 therefore a subsequence of A067251 (Numbers with no trailing zeros in decimal representation).
Union of this sequence with A005408 (The odd numbers) gives A067251.
Union of this sequence with A045572 (Numbers that are odd but not divisible by 5) gives A047201.
The even numbers divisible by 5 are A008592 (Multiples of 10).
FORMULA
a(n) = 2*A047201(n).
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
a(n) = 2*(n+floor((n-1)/4)). - Aaron J Grech, Sep 28 2024
E.g.f.: (4 - cos(x) + (5*x - 3)*cosh(x) + sin(x) + (5*x - 2)*sinh(x))/2. - Stefano Spezia, Sep 28 2024
MATHEMATICA
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 *)
PROG
(BASIC)
for n=1 to 199
if n mod 5 <> 0 and n mod 2 <> 1 then print str$(n)+", ";
next n
print
(PARI) A217562(n)=(n-1)*5\2+2 \\ - M. F. Hasler, Oct 07 2012
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jeremy Gardiner, Oct 06 2012
STATUS
approved