A392682 Primes p(k) > 3 such that, for every integer 1 < m < k (except m = k - 2 if p(k) > 5), there exists a set of m distinct primes < p(k) the sum of whose reciprocals forms a fraction that has a numerator divisible by p(k).

5, 19, 109

Offset

1,1

Comments

Conjecture: this is the intersection of A006512 and A293457.

a(4) > 10^8.

Links

Table of n, a(n) for n=1..3.

Arkadiusz Wesolowski, Examples of sets for a(3) = 109

Example

Examples of sets for a(2) = 19:
  {2, 17},
  {11, 13, 17},
  {2, 3, 5, 7},
  {3, 5, 7, 11, 13},
  {2, 3, 5, 7, 11, 13, 17}.

Crossrefs

Cf. A000720, A006512, A293457.

Sequence in context: A280067 A158615 A321652 * A384822 A088180 A370459

Adjacent sequences: A392679 A392680 A392681 * A392683 A392684 A392685

Keyword

nonn,bref,hard,more

Author

Arkadiusz Wesolowski, Jan 19 2026

Status

approved