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 1-3 of 3 results.

A369946 a(n) is the minimal determinant of an n X n Hankel matrix using the first 2*n - 1 prime numbers.

Original entry on oeis.org

1, 2, -19, -1115, -57935, -5696488, -2307021183
Offset: 0

Views

Author

Stefano Spezia, Feb 06 2024

Keywords

Examples

			a(2) = -19:
  2, 5;
  5, 3.
a(3) = -1115:
   3,  7, 11;
   7, 11,  2;
  11,  2,  5.
a(4) = -57935:
   7,  5, 17,  2;
   5, 17,  2,  3;
  17,  2,  3, 11;
   2,  3, 11, 13.

Links

Crossrefs

Cf. A024356, A368351.
Cf. A369947 (maximal), A350933 (maximal absolute value), A369949, A350939 (minimal permanent).

Programs

  • Mathematica
    a[n_] := Min[Table[Det[HankelMatrix[Join[Drop[per = Part[Permutations[Prime[Range[2 n - 1]]], i], n], {Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]
  • PARI
    a(n) = my(v=[1..2*n-1], m=+oo, d); forperm(v, p, d = matdet(matrix(n, n, i, j, prime(p[i+j-1]))); if (dMichel Marcus, Feb 08 2024
  • Python
    from itertools import permutations
from sympy import primerange, prime, Matrix
def A369946(n): return min(Matrix([p[i:i+n] for i in range(n)]).det() for p in permutations(primerange(prime((n<<1)-1)+1))) if n else 1 # Chai Wah Wu, Feb 12 2024

Extensions

a(6) from Michel Marcus, Feb 08 2024

A368352 a(n) is the maximal determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1.

Original entry on oeis.org

1, 1, 5, 42, 2294, 71753, 2737409, 114381074
Offset: 0

Views

Author

Stefano Spezia, Dec 22 2023

Keywords

Examples

			a(2) = 5:
  3, 1;
  1, 2.
a(3) = 42:
  2, 5, 3;
  5, 3, 4;
  3, 4, 1.
a(4) = 2294:
  2, 3, 6, 7;
  3, 6, 7, 1;
  6, 7, 1, 5;
  7, 1, 5, 4.

Links

Crossrefs

Cf. A350931 (maximal absolute value), A368351 (minimal).
Cf. A350937 (minimal permanent), A350938 (maximal permanent).

Extensions

a(6)-a(7) from Lucas A. Brown, Aug 26 2024

A369942 a(n) is the number of distinct values of the determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1.

Original entry on oeis.org

1, 1, 3, 49, 1480, 50522, 2517213
Offset: 0

Views

Author

Stefano Spezia, Feb 06 2024

Keywords

Links

Crossrefs

Cf. A350931, A368351, A368352.

Programs

  • Mathematica
    a[n_] := CountDistinct[Table[Det[HankelMatrix[Join[Drop[per = Part[Permutations[Range[2 n - 1]], i], n],{Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]
  • PARI
    a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matdet(matrix(n, n, i, j, p[i+j-1])));); #Set(list); \\ Michel Marcus, Feb 08 2024
  • Python
    from itertools import permutations
from sympy import Matrix
def A369942(n): return len({Matrix([p[i:i+n] for i in range(n)]).det() for p in permutations(range(1,n<<1))}) # Chai Wah Wu, Feb 12 2024

Extensions

a(6) from Michel Marcus, Feb 08 2024
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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