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

Author

Jeremy Gardiner, Oct 06 2012

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

BASIC

for n=1 to 199
if n mod 5 <> 0 and n mod 2 <> 1 then print str$(n)+", ";
next n
print

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

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 *)

PARI

A217562(n)=(n-1)*5\2+2 \\ M. F. Hasler, Oct 07 2012

Python

def A217562(n): return (5*n-1>>1)&-2 # Chai Wah Wu, Apr 21 2025

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