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.

A111392 a(n) = Product_{i=1..n-1} (Product_{k=1..i} p_k + Product_{k=i+1..n} p_k).

Original entry on oeis.org

2, 5, 187, 162319, 10697595389, 63619487169453143, 74365399061678006800073593, 11864736003419293844093922527852416537, 601642845102734414280661105098046392912578705726003
Offset: 1

Views

Author

Yasutoshi Kohmoto, Nov 08 2005

Keywords

Comments

This sequence gives another proof that there are infinitely many primes. Let N = Product_{1<=i
a(1) could also be chosen to be 1.

Links

Crossrefs

Cf. A024451, A112404.

Programs

  • Maple
    a:=n->mul(mul(ithprime(k),k=1..i)+mul(ithprime(k),k=i+1..n),i=1..n-1): 2,seq(a(n),n=2..10); # Muniru A Asiru, Dec 06 2018
  • Mathematica
    Join[{2}, Rest[f[n_]:=Product[(Product[Prime[k], {k, i}] + Product[Prime[k], {k, i + 1, n}]), {i, n - 1}]; Array[f, 10] ]] (* Robert G. Wilson v, Nov 12 2005 *)
  • PARI
    t=10; for(n=2, t, print1(prod(i=1, n-1, prod(k=1,i,prime(k)) + prod(k=i+1,n,prime(k))), ", ")); \\ Gerald McGarvey, Nov 12 2005

Extensions

Corrected and extended by Gerald McGarvey and Robert G. Wilson v, Nov 12 2005

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