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A293292 Numbers with last digit less than 5 (in base 10). 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified December 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)