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
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]
-
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
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]
-
a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
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
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]
-
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]]
A374345
a(n) is the maximal permanent 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, 5, 59, 2454, 177998, 36960008, 7670953632, 2822399976144, 1061085324952592, 598646324654443008
Offset: 0
a(5) = 177998:
[1, 7, 5, 3, 2]
[7, 1, 7, 5, 3]
[5, 7, 1, 7, 5]
[3, 5, 7, 1, 7]
[2, 3, 5, 7, 1]
-
a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
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
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]
-
a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
A374619
a(n) is the number of distinct values 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, 1, 2, 6, 22, 120, 717, 5039, 40312, 362874
Offset: 0
-
a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]
Showing 1-6 of 6 results.