A349999 Least number m of primes that must have appeared in an interval [j^2, (j+1)^2], such that all intervals [k^2, (k+1)^2], k>j contain more than m primes. The corresponding values of j are A349998.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 19, 22, 24, 26, 27, 28, 29, 30, 32, 33, 35, 36, 38, 39, 40, 41, 44, 45, 47, 51, 54, 56, 63, 65, 68, 70, 71, 78, 80, 85, 94, 99, 106, 107, 114, 115, 120, 121, 127, 133, 138, 146, 154, 155, 164, 168, 169, 175, 176, 177

Offset: 1

Author

Hugo Pfoertner, Dec 09 2021

Keywords

• nonn

Comments

All terms are empirical (see the graph of A014085 for the limited width of the scatter band), but supporting the validity of Legendre's conjecture that there is always a prime between n^2 and (n+1)^2.

The terms are determined by searching from large to small indices in A014085 for new minima.

Examples

			See A349997 and A349998.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..2414

Crossrefs

Cf. A014085, A084597, A349997, A349998.

Cf. A333846, A349996.

Formula

a(n) = A014085(A349998(n)).

A014085(k) > a(n) for k > A349998(n).

A014085(k) >= a(n) for k >= A349997(n).