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.

A374386 a(n) is the minimal determinant 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, 24, -324, -15164, -1453072, -161765904, -37905894000, -1376219654680, -718058901423168, -163742479201610036
Offset: 0

Views

Author

Stefano Spezia, Jul 07 2024

Keywords

Examples

			a(5) = -15164:
  [0, 2, 7, 3, 5]
  [2, 0, 2, 7, 3]
  [7, 2, 0, 2, 7]
  [3, 7, 2, 0, 2]
  [5, 3, 7, 2, 0]
		

Crossrefs

Cf. A374387 (maximal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).
Cf. A374068 (minimal permanent), A374390 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

Extensions

a(11) from Giorgos Kalogeropoulos, Jul 10 2024

A374387 a(n) is the maximal determinant 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, 129, 3340, 2287607, 162104000, 16943055268, 4059346088384, 474967482901952, 221630954408019520
Offset: 0

Views

Author

Stefano Spezia, Jul 07 2024

Keywords

Examples

			a(5) = 3340:
  [0, 5, 7, 3, 2]
  [5, 0, 5, 7, 3]
  [7, 5, 0, 5, 7]
  [3, 7, 5, 0, 5]
  [2, 3, 7, 5, 0]
		

Crossrefs

Cf. A374386 (minimal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).
Cf. A374068 (minimal permanent), A374390 (maximal permanent).

Programs

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

Extensions

a(11) from Giorgos Kalogeropoulos, Jul 10 2024

A374388 a(n) is the maximal absolute value of the determinant 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, 324, 15164, 2287607, 162104000, 37905894000, 4059346088384, 718058901423168, 221630954408019520
Offset: 0

Views

Author

Stefano Spezia, Jul 07 2024

Keywords

Examples

			a(5) = 15164:
  [0, 2, 7, 3, 5]
  [2, 0, 2, 7, 3]
  [7, 2, 0, 2, 7]
  [3, 7, 2, 0, 2]
  [5, 3, 7, 2, 0]
		

Crossrefs

Cf. A374386 (minimal), A374387 (maximal), A374389 (minimal nonzero absolute value).
Cf. A374068 (minimal permanent), A374390 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

Formula

a(n) = max(abs(A374386(n)), A374387(n)).

Extensions

a(11) from Giorgos Kalogeropoulos, Jul 12 2024

A374389 a(n) is the minimal absolute value of the determinant of a nonsingular 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

4, 24, 116, 192, 1079, 664, 720, 216
Offset: 2

Views

Author

Stefano Spezia, Jul 07 2024

Keywords

Comments

The offset is 2 because for n = 1 the unique symmetric Toeplitz matrix is singular.

Examples

			a(5) = 192:
  [0, 5, 3, 2, 7]
  [5, 0, 5, 3, 2]
  [3, 5, 0, 5, 3]
  [2, 3, 5, 0, 5]
  [7, 2, 3, 5, 0]
		

Crossrefs

Cf. A374386 (minimal), A374387 (maximal), A374388 (maximal absolute value).
Cf. A374068 (minimal permanent), A374390 (maximal permanent).

Programs

  • Mathematica
    a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}],Positive]]; Array[a,8,2]
Showing 1-4 of 4 results.