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]]
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
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]
-
a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
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
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]
-
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]
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
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]
-
a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
A374620
a(n) is the number of distinct values 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, 1, 1, 2, 6, 24, 120, 717, 5040, 40314, 362874
Offset: 0
-
a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]
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