A217562 Even numbers not divisible by 5.

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).

Links

Jeremy Gardiner, Table of n, a(n) for n = 1..4000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

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

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

Cf. A005408, A005843, A045572, A047201, A067251.

Sequence in context: A058817 A328593 A254748 * A088879 A316470 A290822

Adjacent sequences: A217559 A217560 A217561 * A217563 A217564 A217565

Keyword

nonn,easy

Author

Jeremy Gardiner, Oct 06 2012

Status

approved