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.

A089612 a(n) = ((-1)^(n+1)*A002425(n)) modulo 5.

Original entry on oeis.org

1, 4, 1, 3, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 2, 1, 4, 1, 3, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 4, 1, 4, 1, 3, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 2, 1, 4, 1, 3, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 2, 1, 4, 1, 3, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 4, 1, 4, 1, 3, 1, 4, 1, 1, 1
Offset: 1

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Author

Benoit Cloitre, Dec 30 2003

Keywords

Crossrefs

Programs

  • Magma
    [Numerator(2/n*(4^n-1)*Bernoulli(2*n)) mod 5: n in [1..100]]; // Vincenzo Librandi, Aug 01 2018
  • Mathematica
    Table[Mod[Numerator[2 / n (4^n - 1) BernoulliB[2 n]], 5], {n, 100}] (* Vincenzo Librandi, Aug 01 2018 *)
  • PARI
    a(n)=numerator(2/n*(4^n-1)*bernfrac(2*n))%5
    
  • PARI
    a(n)=if(n%2, 1, 2*2^valuation(n,2) % 5); \\ Andrew Howroyd, Aug 01 2018
    

Formula

Let S(1) = {1, 4} and S(n+1) = S(n)*S'(n), where S'(n) is obtained from S(n) by changing last term using the cyclic permutation 4->3->1->2->4; sequence is S(infinity).
Multiplicative with a(2^e) = 2^(e + 1) mod 5, a(p^e) = 1 for odd prime p. - Andrew Howroyd, Aug 01 2018
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 21/10. - Amiram Eldar, Nov 10 2022