A293292 Numbers with last digit less than 5 (in base 10).

0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 70, 71, 72, 73, 74, 80, 81, 82, 83, 84, 90, 91, 92, 93, 94, 100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130

Offset

1,3

Comments

Equivalently, numbers k such that floor(k/5) = 2*floor(k/10).

After 0, partial sums of A010122 starting from the 2nd term.

The sequence differs from A007091 after a(25).

Also numbers k such that floor(k/5) is even. - Peter Luschny, Oct 05 2017

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x^2*(1 + x + x^2 + x^3 + 6*x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

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

a(n) = (n-1) + 5*floor((n-1)/5) = 10*floor((n-1)/5) + ((n-1) mod 5).

a(n) = A257145(n+2) - A239229(n-1). - R. J. Mathar, Oct 05 2017

Maple

select(k -> type(floor(k/5), even), [$0..130]); # Peter Luschny, Oct 05 2017

Mathematica

Table[n + 5 Floor[n/5], {n, 0, 70}]
Reap[For[k = 0, k <= 130, k++, If[Floor[k/5] == 2*Floor[k/10], Sow[k]]]][[2, 1]] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 10}, 66] (* Jean-François Alcover, Oct 05 2017 *)

Prog

(Magma) [n: n in [0..130] | n mod 10 lt 5];
(Magma) [n: n in [0..130] | IsEven(Floor(n/5))];
(Magma) [n+5*Floor(n/5): n in [0..70]];
(PARI) concat(0, Vec(x^2*(1 + x + x^2 + x^3 + 6*x^4) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^70))) \\ Colin Barker, Oct 05 2017
(PARI) select(k->floor(k/5) == 2*floor(k/10), vector(1000, k, k)) \\ Colin Barker, Oct 05 2017
(Python 3) [k for k in range(131) if (k//5) % 2 == 0] # Peter Luschny, Oct 05 2017
(Sage) [k for k in (0..130) if 2.divides(floor(k/5))] # Peter Luschny, Oct 05 2017

Crossrefs

Cf. A010122, A239229, A257145, A293481 (complement).

Sequences of the type floor(n/d) = (10/d)*floor(n/10), where d is a factor of 10: A008592 (d=1), A197652 (d=2), this sequence (d=5), A001477 (d=10).

Sequences of the type n + r*floor(n/r): A005843 (r=1), A042948 (r=2), A047240 (r=3), A047476 (r=4), this sequence (r=5).

Sequence in context: A098892 A174139 A037325 * A037469 A007091 A058185

Adjacent sequences: A293289 A293290 A293291 * A293293 A293294 A293295

Keyword

nonn,base,easy

Author

Bruno Berselli, Oct 05 2017

Extensions

Definition by David A. Corneth, Oct 05 2017

Status

approved