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 1-5 of 5 results.

A374340 a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

Original entry on oeis.org

1, 1, -3, 8, -21, -12167, -1708047, -116428560, -33081320935, -1098860747703, -579469550006151
Offset: 0

Views

Author

Stefano Spezia, Jul 05 2024

Keywords

Examples

			a(5) = -12167:
  [1, 2, 7, 3, 5]
  [2, 1, 2, 7, 3]
  [7, 2, 1, 2, 7]
  [3, 7, 2, 1, 2]
  [5, 3, 7, 2, 1]
		

Crossrefs

Cf. A374341 (maximal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

A374341 a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

Original entry on oeis.org

1, 1, -3, 15, 259, 1608, 1582152, 157042600, 11778545664, 3336975844504, 440384712302421
Offset: 0

Views

Author

Stefano Spezia, Jul 05 2024

Keywords

Examples

			a(5) = 1608:
  [1, 7, 2, 3, 5]
  [7, 1, 7, 2, 3]
  [2, 7, 1, 7, 2]
  [3, 2, 7, 1, 7]
  [5, 3, 2, 7, 1]
		

Crossrefs

Cf. A374340 (minimal), A374342 (maximal absolute value), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

A374342 a(n) is the maximal absolute value of the determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

Original entry on oeis.org

1, 1, 3, 15, 259, 12167, 1708047, 157042600, 33081320935, 3336975844504, 579469550006151
Offset: 0

Views

Author

Stefano Spezia, Jul 05 2024

Keywords

Examples

			a(5) = 12167:
  [1, 2, 7, 3, 5]
  [2, 1, 2, 7, 3]
  [7, 2, 1, 2, 7]
  [3, 7, 2, 1, 2]
  [5, 3, 7, 2, 1]
		

Crossrefs

Cf. A374340 (minimal), A374341 (maximal), A374343 (minimal nonzero absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

Formula

a(n) = max(abs(A374340(n)),A374341(n)).

A374343 a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the first n-1 primes off-diagonal.

Original entry on oeis.org

1, 1, 3, 8, 7, 32, 81, 504, 327, 95
Offset: 0

Views

Author

Stefano Spezia, Jul 05 2024

Keywords

Examples

			a(5) = 32:
  [1, 3, 2, 5, 7]
  [3, 1, 3, 2, 5]
  [2, 3, 1, 3, 2]
  [5, 2, 3, 1, 3]
  [7, 5, 2, 3, 1]
		

Crossrefs

Cf. A374340 (minimal), A374341 (maximal), A374342 (maximal absolute value), A374067 (minimal permanent), A374345 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}],Positive]]; Join[{1},Array[a,10]]

A374390 a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

Original entry on oeis.org

1, 0, 4, 36, 1936, 144260, 31972988, 6800311204, 2560967581304, 975834087080060, 557171087172087364
Offset: 0

Views

Author

Stefano Spezia, Jul 07 2024

Keywords

Examples

			a(5) = 144260:
  [0, 7, 5, 3, 2]
  [7, 0, 7, 5, 3]
  [5, 7, 0, 7, 5]
  [3, 5, 7, 0, 7]
  [2, 3, 5, 7, 0]
		

Crossrefs

Cf. A374345.
Cf. A374068 (minimal permanent).

Programs

  • Mathematica
    a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
Showing 1-5 of 5 results.