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A047217
Numbers that are congruent to {0, 1, 2} mod 5.
25
0, 1, 2, 5, 6, 7, 10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40, 41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 60, 61, 62, 65, 66, 67, 70, 71, 72, 75, 76, 77, 80, 81, 82, 85, 86, 87, 90, 91, 92, 95, 96, 97, 100, 101, 102, 105, 106, 107, 110, 111
OFFSET
1,3
COMMENTS
Also, the only numbers that are eligible to be the sum of two 4th powers (A004831). - Cino Hilliard, Nov 23 2003
Nonnegative m such that floor(2*m/5) = 2*floor(m/5). - Bruno Berselli, Dec 09 2015
The sequence lists the indices of the multiples of 5 in A007531. - Bruno Berselli, Jan 05 2018
LINKS
Mohammed Yaseen, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
FORMULA
a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k)=5*3^(k-1) for k>0. - Philippe Deléham, Oct 22 2011
G.f.: x^2*(1+x+3*x^2)/(1-x)^2/(1+x+x^2). - Colin Barker, Feb 17 2012
a(n) = 5 + a(n-3) for n>3. - Robert Israel, Sep 02 2014
a(n) = floor((5/4)*floor(4*(n-1)/3)). - Bruno Berselli, May 03 2016
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (15*n-21-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3*k) = 5*k-3, a(3*k-1) = 5*k-4, a(3*k-2) = 5*k-5. (End)
a(n) = n - 1 + 2*floor((n-1)/3). - Bruno Berselli, Feb 06 2017
Sum_{n>=2} (-1)^n/a(n) = sqrt(1-2/sqrt(5))*Pi/5 + 3*log(2)/5. - Amiram Eldar, Dec 10 2021
MAPLE
seq(op([5*i, 5*i+1, 5*i+2]), i=0..100); # Robert Israel, Sep 02 2014
MATHEMATICA
Select[Range[0, 120], MemberQ[{0, 1, 2}, Mod[#, 5]]&] (* Harvey P. Dale, Jan 20 2012 *)
PROG
(PARI) a(n)=n--\3*5+n%3 \\ Charles R Greathouse IV, Oct 22 2011
(PARI) concat(0, Vec(x^2*(1+x+3*x^2)/(1-x)^2/(1+x+x^2) + O(x^100))) \\ Altug Alkan, Dec 09 2015
(PARI) is(n) = n%5 < 3 \\ Felix Fröhlich, Jan 05 2018
(Magma) I:=[0, 1, 2, 5]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]: // Vincenzo Librandi, Apr 25 2012
(Magma) &cat [[5*n, 5*n+1, 5*n+2]: n in [0..30]]; // Bruno Berselli, Dec 09 2015
CROSSREFS
Cf. A007531, A030341, A004831 (two 4th powers).
Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.
Sequence in context: A057694 A049303 A177987 * A219650 A039015 A037453
KEYWORD
nonn,easy
STATUS
approved