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.

A125503 Smallest number k such that the numerator of the generalized harmonic number H(k,n) = Sum_{i=1..k} 1/i^n is a prime.

Original entry on oeis.org

2, 2, 3, 2, 23, 73, 15, 2, 3, 5, 13, 57, 3, 171, 5, 2, 21, 7, 55, 8902, 26, 1298, 115, 139, 3, 2019, 3, 4, 3, 15, 56, 177
Offset: 1

Views

Author

Alexander Adamchuk, Dec 28 2006, Jan 31 2007

Keywords

Comments

a(n) = 2 for n = {1,2,4,8,16,...}. Corresponding Fermat primes A019434.
a(n) = 3 for n = {3,9,13,25,27,29,95,107,153,159,...}.
a(n) = 5 for n = {10,15,60,90,197,209,...}.
a(n) = 7 for n = {18,47,112,155,273,...}.
a(n) = 15 for n = {7,30,43,...}.
a(21) = 26. a(28) = 4. a(31) = 56. a(144) = 9.
From Alexander Adamchuk, Apr 18 2010: (Start)
a(22)-a(25) = {1298,115,139,3}.
a(27)-a(32) = {3,4,3,15,56,177}.
a(n) = 3 for all n>2 listed in A125706. (End)
a(26) = 2019. - Alexander Adamchuk, Apr 26 2010
a(20) > 3000. - Michael S. Branicky, Jun 25 2022

Crossrefs

Programs

  • Mathematica
    Do[n = 1; f = 0; While[Not[PrimeQ[Numerator[f]]], f = f + 1/n^x; n++ ]; Print[{x, n - 1}], {x, 1, 25}] (* Alexander Adamchuk, Apr 18 2010 *)
  • PARI
    a(n) = my(k=1); while (!ispseudoprime(numerator(sum(i=1, k, 1/i^n))), k++); k; \\ Michel Marcus, Jun 04 2022
    
  • Python
    from sympy import isprime
    from fractions import Fraction
    def a(n):
        Hkn, k = Fraction(1, 1), 1
        while not isprime(Hkn.numerator):
            k += 1
            Hkn += Fraction(1, k**n)
        return k
    print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Jun 11 2022

Extensions

a(22)-a(25) from Alexander Adamchuk, Apr 18 2010
a(26)-a(32) from Alexander Adamchuk, Apr 26 2010
Incorrect a(20) removed by Michael S. Branicky, Jun 25 2022
a(20) = 8902 from Michael S. Branicky, Jun 12 2023