cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A083054 a(n) = floor(sqrt(3)*n) - 3*floor(n/sqrt(3)).

Original entry on oeis.org

1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 0, 1
Offset: 1

Views

Author

Benoit Cloitre, Apr 18 2003

Keywords

Links

Crossrefs

Cf. A083035, A083038, A083055, A083056, A083057.
Cf. A022383 (floor(n*sqrt(3))).

Programs

  • PARI
    {a(n)=if(n<1, 0, sqrtint(3*n^2)-3*sqrtint(n^2\3))} /* Michael Somos, Aug 31 2006 */

Formula

a(n) = floor(n*sqrt(3)) mod 3. - T. D. Noe, Oct 11 2006

A083055 a(n) = cardinality{ k<=n / A083054(k)=1}.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 25, 25
Offset: 1

Views

Author

Benoit Cloitre, Apr 18 2003

Keywords

Links

Crossrefs

Cf. A083038, A083054, A083056, A083057.

Programs

  • PARI
    {a(n)=if(n<1,0, sum(k=1,n,sqrtint(3*k^2)-3*sqrtint(k^2\3)==1))} /* Michael Somos, Aug 31 2006 */

Formula

a(n) = n/3 + O(n) (it seems O(n) could be replaced with O(log(n))).

A083056 a(n) = 3*A083055(n)-n.

Original entry on oeis.org

2, 1, 0, -1, -2, 0, -1, 1, 0, -1, 1, 0, 2, 1, 3, 2, 1, 3, 2, 4, 3, 2, 1, 0, 2, 1, 3, 2, 1, 0, -1, 1, 0, 2, 1, 0, 2, 1, 3, 2, 1, 0, -1, 1, 0, 2, 1, 0, -1, -2, 0, -1, 1, 0, -1, -2, -3, -1, -2, 0, -1, -2, 0, -1, 1, 0, -1, -2, -3, -1, -2, 0, -1, -2, -3, -4, -2, -3, -1, -2, -3, -1, -2, 0, -1, 1, 0, -1, 1, 0, 2, 1, 0, -1, -2, 0, -1, 1, 0, -1, -2, -3, -1, -2, 0
Offset: 1

Views

Author

Benoit Cloitre, Apr 18 2003

Keywords

Links

Crossrefs

Cf. A083038, A083054, A083055, A083057.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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