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.

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A320624 a(n) = (A006134((prime(n)-1)/2) - Legendre(prime(n), 3))/prime(n).

Original entry on oeis.org

1, 2, 4, 32, 98, 1034, 3484, 41582, 1868198, 6751460, 330246410, 4522217312, 16829506610, 235344648416, 12559206444236, 683534482499900, 2599887148071402, 144419015585768252, 2117118216002111198, 8120930597438173620
Offset: 2

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Author

Jianing Song, Oct 18 2018

Keywords

Comments

a(n) is always an integer.
Primes p such that p^2 divides A006134((p-1)/2) - Legendre(p, 3) are p = 103, ... What's the next?

Crossrefs

Cf. A006134, A102283, A320626.

Programs

  • PARI
    A006134(n) = sum(k=0, n, binomial(2*k,k))
a(n) = my(p=prime(n)); (A006134((p-1)/2) - kronecker(p,3))/p

Formula

a(2) = (binomial(0, 0) + binomial(2, 1))/3 = 3/3 = 1.
a(3) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + 1)/5 = 10/5 = 2.
a(4) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + binomial(6, 3) - 1)/7 = 28/7 = 4.
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