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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also, the only numbers that are eligible to be the sum of two 4th powers. - 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

Vincenzo Librandi, 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+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

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.

Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.

Sequence in context: A057694 A049303 A177987 * A219650 A039015 A037453

Adjacent sequences:  A047214 A047215 A047216 * A047218 A047219 A047220

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 20 12:34 EST 2020. Contains 332076 sequences. (Running on oeis4.)