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

5, 6, 7, 8, 9, 15, 16, 17, 18, 19, 25, 26, 27, 28, 29, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 65, 66, 67, 68, 69, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 95, 96, 97, 98, 99, 105, 106, 107, 108, 109, 115, 116, 117, 118, 119, 125, 126, 127, 128, 129

Offset

1,1

Comments

Equivalently, numbers k such that floor(k/5) is odd.

Also numbers k such that ceiling(-k/5) is odd. - Peter Luschny, Oct 10 2017

Links

Colin Barker, Table of n, a(n) for n = 1..500

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

Formula

G.f.: x*(5 + x + x^2 + x^3 + x^4 + x^5)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-5) - a(n-6).

a(n) = A293292(n) + 5.

Maple

select(n -> type(ceil(-n/5), odd), [$0..130]); # Peter Luschny, Oct 10 2017

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {5, 6, 7, 8, 9, 15}, 70]
(* Second program: *)
Select[Range[129], Mod[#, 10] >= 5 &] (* Jean-François Alcover, Oct 10 2017 *)

Prog

(Magma) [n: n in [0..150] | n mod 10 ge 5];
(PARI) select(k -> (k\5) % 2, vector(130, k, k)) \\ Peter Luschny, Oct 10 2017
(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
(Python) [k for k in range(130) if (k//5) % 2 == 1] # Peter Luschny, Oct 10 2017
(Sage) [k for k in (0..130) if not 2.divides(k//5)] # Peter Luschny, Oct 10 2017

Crossrefs

Complement of A293292.

Cf. A010122 (first differences, after 3).

Sequence in context: A121537 A285219 A047577 * A174138 A108401 A125298

Adjacent sequences: A293478 A293479 A293480 * A293482 A293483 A293484

Keyword

nonn,base,easy

Author

Bruno Berselli, Oct 10 2017

Status

approved