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A047212 Numbers that are congruent to {0, 2, 4} mod 5. 28
0, 2, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 25, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 65, 67, 69, 70, 72, 74, 75, 77, 79, 80, 82, 84, 85, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 104, 105, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also numbers k such that k*(k+1)*(k+3) is divisible by 5. - Bruno Berselli, Dec 28 2017

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

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

FORMULA

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

G.f.: x^2*(2 + 2*x + x^2)/((1 - x)^2*(1 + x + x^2)). - Bruno Berselli, Mar 31 2011

a(n) = floor((5*n-3)/3). - Gary Detlefs, May 14 2011

a(n) = n + ceiling(2*(n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012

From Wesley Ivan Hurt, Jun 14 2016: (Start)

a(n) = (15*n - 12 + 3*cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/9.

a(3*k) = 5*k-1, a(3*k-1) = 5*k-3, a(3*k-2) = 5*k-5. (End)

MAPLE

A047212:=n->floor((5*n-3)/3); seq(A047212(n), n=1..100); # Wesley Ivan Hurt, Nov 25 2013

MATHEMATICA

Select[Range[0, 200], MemberQ[{0, 2, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)

PROG

(MAGMA) [n : n in [0..140] | n mod 5 in [0, 2, 4]]; // Vincenzo Librandi, Mar 31 2011

(MAGMA) &cat[[n, n+2, n+4]: n in [0..90 by 5]]; // Bruno Berselli, Mar 31 2011

(PARI) a(n)=n\3*5+[-1, 0, 2][n%3+1] \\ Charles R Greathouse IV, Mar 29 2012

CROSSREFS

Cf. A047209, A047211.

Sequence in context: A184656 A286989 A226720 * A121347 A303589 A106829

Adjacent sequences:  A047209 A047210 A047211 * A047213 A047214 A047215

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 20 08:16 EST 2018. Contains 317385 sequences. (Running on oeis4.)