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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A334614 a(n) = pi(prime(n) - n) + n, where pi is the prime counting function.

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 11, 13, 15, 18, 19, 21, 22, 24, 26, 28, 30, 32, 34, 35, 36, 38, 40, 42, 45, 47, 48, 50, 51, 53, 55, 57, 60, 61, 65, 66, 67, 68, 70, 72, 74, 76, 77, 79, 81, 82, 85, 88, 89, 91, 93, 94, 95, 99, 101, 102, 104, 105, 106, 107, 108, 112, 116, 117
Offset: 1

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Author

Ya-Ping Lu, Sep 08 2020

Keywords

Comments

It can be shown that a(n) > a(n-1) >= 1 and a(n) <= 2*n - 1 < 2*n (see proofs in the Links section).

Crossrefs

Programs

  • Mathematica
    Table[PrimePi[Prime[n] - n] + n, {n, 1, 64}] (* Amiram Eldar, Sep 09 2020 *)
  • PARI
    a(n) = n + primepi(prime(n) - n); \\ Michel Marcus, Sep 09 2020
  • Python
    from sympy import prime, primepi
    for n in range(1, 100001):
        a_n = primepi(prime(n) - n) + n
        print(a_n)
    

Formula

a(n) = A000720(A014689(n)) + n.
a(n) = A065328(n) + n. - Michel Marcus, Sep 12 2020
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