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.

A203315 Vandermonde determinant of the first n odd primes.

Original entry on oeis.org

1, 2, 16, 3072, 2949120, 118908518400, 30684105356083200, 509012486930992988160000, 1448974328493266972309245132800000, 24498250851046882007528282887645298688000000, 120709538882209643641596013856771385957962848665600000000
Offset: 1

Views

Author

Clark Kimberling, Jan 01 2012

Keywords

Comments

Each term divides its successor, as in A203316, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203317.

Examples

			v(3)=(5-3)(7-3)(7-5)=16.
		

Crossrefs

Programs

  • Maple
    Primes:=3:
    A[1]:= 1:
    for n from 2 to 20 do
      Primes:=  Primes, ithprime(n+1);
      A[n]:= A[n-1] * mul(Primes[n]-Primes[i],i=1..n-1);
    od:
    seq(A[i],i=1..20);# Robert Israel, Apr 08 2019
  • Mathematica
    f[j_] := Prime[j + 1]; z = 17;
    v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
    d[n_] := Product[(i - 1)!, {i, 1, n}]
    Table[v[n], {n, 1, z}]                  (* A203315 *)
    Table[v[n + 1]/(2 v[n]), {n, 1, z - 1}] (* A203316 *)
    Table[v[n]/d[n], {n, 1, 20}]            (* A203317 *)

A203316 a(n) = v(n+1)/(2*v(n)), where v=A203315.

Original entry on oeis.org

1, 4, 96, 480, 20160, 129024, 8294400, 1423319040, 8453652480, 2463635865600, 89117289676800, 660834091008000, 63038756487168000, 20712734274355200000, 4023397460155878604800, 27460572284725493760000
Offset: 1

Views

Author

Clark Kimberling, Jan 01 2012

Keywords

Crossrefs

Programs

  • Mathematica
    f[j_] := Prime[j + 1]; z = 17;
    v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
    d[n_] := Product[(i - 1)!, {i, 1, n}]
    Table[v[n], {n, 1, z}]                  (* A203315 *)
    Table[v[n + 1]/(2 v[n]), {n, 1, z - 1}] (* A203316 *)
    Table[v[n]/d[n], {n, 1, 20}]            (* A203317 *)

Extensions

Definition corrected by Georg Fischer, Nov 26 2021

A203526 v(n)/A000178(n); v=A203524 and A000178=(superfactorials).

Original entry on oeis.org

1, 8, 480, 322560, 1857945600, 137339338752000, 90498933234597888000, 806410654352196092559360000, 151104996166246050391298219704320000, 278316545034703677313682486677538340864000000
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2012

Keywords

Comments

It is conjectured that every term of A203526 is an integer.

Crossrefs

Programs

  • Mathematica
    f[j_] := Prime[j + 1]; z = 17;
    v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
    d[n_] := Product[(i - 1)!, {i, 1, n}]    (* A000178 *)
    Table[v[n], {n, 1, z}]                   (* A203524 *)
    Table[v[n + 1]/(8 v[n]), {n, 1, z - 1}]  (* A203525 *)
    Table[v[n]/d[n], {n, 1, 20}]             (* A203526 *)
Showing 1-3 of 3 results.