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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
OFFSET
1,2
COMMENTS
Also numbers k such that k*(k+1)*(k+3) is divisible by 5. - Bruno Berselli, Dec 28 2017
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)
Sum_{n>=2} (-1)^n/a(n) = log(2)/5 + arccosh(7/2)/(2*sqrt(5)) - sqrt(1-2*sqrt(5)/5)*Pi/5. - Amiram Eldar, Dec 10 2021
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
Sequence in context: A184656 A286989 A226720 * A358845 A121347 A303589
KEYWORD
nonn,easy
STATUS
approved