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
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_]:=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
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]]
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]]
Showing 1-5 of 5 results.