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 1-4 of 4 results.

A003509 Let k(m) denote the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros. The sequence gives the index n of the first term in each string of equal entries in the {k(m)} sequence (see A155934).

Original entry on oeis.org

2, 3, 7, 13, 21, 31
Offset: 2

Views

Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A005991 (index of last term), A155934.

Extensions

Title made more specific by Sean A. Irvine, Jun 04 2015

A005991 Let k(m) denote the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros. The sequence gives the index n of the last term in each string of equal entries in the {k(m)} sequence (see A155934).

Original entry on oeis.org

2, 6, 12, 20, 30, 43
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			Since k(2) = 2 then a(1) = 2
Since k(3) = k(4) = k(5) = k(6) = 3 then a(2) = 6
Since k(7) = k(8) = ... = k(12) = 4 then a(3) = 12
Since k(13) = k(14) = ... = k(20) = 5 then a(4) = 20
Since k(21) = k(22) = ... = k(30) = 6 then a(5) = 30
Since k(31) = k(32) = ... = k(43) = 7 then a(6) = 43

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A003509 (index of first term), A155934.

Formula

a(n) = A003509(n + 1) - 1. - Sean A. Irvine, Jun 04 2015

Extensions

Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008

A368941 a(n) = floor(3/2 + sqrt(n)).

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
Offset: 0

Views

Author

Eric W. Weisstein, Jan 10 2024

Keywords

Comments

Burning number of the n-ladder (for n >= 1), n-Moebius ladder (for n >= 3), and n-prism (for n >= 3) graphs.

Links

Crossrefs

Sequence agrees with the known terms of A155934.
Cf. A000194, A003059.

Programs

  • Mathematica
    Table[Floor[3/2 + Sqrt[n]], {n, 50}]
Floor[3/2 + Sqrt[Range[50]]]
CoefficientList[Series[(1 + QPochhammer[-x^2, x^4]  QPochhammer[x^8, x^8])/(1 - x), {x, 0, 50}], x]

Formula

a(n) = A000194(n) + 1. - Andrew Howroyd, Jan 10 2024
G.f.: x*(1 + QPochhammer(-x^2, x^4)*QPochhammer(x^8, x^8))/(1 - x).

Extensions

Terms a(26) and beyond from Andrew Howroyd, Jan 10 2024

A289189 Upper bound for certain restricted sumsets.

Original entry on oeis.org

3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
Offset: 1

Views

Author

Robert Price, Aug 13 2017

Keywords

References

  • Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, Manuscript, May 2017. See Corollary C.56.

Links

Crossrefs

Cf. A155934, A288583, A289434.

Programs

  • Mathematica
    Table[Floor[(Sqrt[4*n + 9] + 3)/2], {n, 100}]

Formula

a(n) = floor( (sqrt(4*n + 9) + 3) / 2).
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.