A349998 Numbers k such that the number of primes in any interval [j^2,(j+1)^2], j>k exceeds the number of primes in the interval [k^2,(k+1)^2].

5, 9, 14, 17, 23, 26, 30, 42, 49, 55, 56, 80, 85, 89, 119, 137, 143, 149, 156, 174, 178, 188, 194, 200, 207, 219, 228, 247, 261, 263, 279, 297, 327, 335, 356, 425, 433, 451, 485, 506, 536, 600, 607, 696, 708, 749, 768, 799, 801, 898, 904, 955, 1015, 1059, 1110

Offset: 1

Author

Hugo Pfoertner, Dec 09 2021

Keywords

• nonn

Comments

All terms are empirical subject to the validity of Legendre's conjecture and the boundedness of the scatter band of A014085. See there for further information.

Examples

			a(1)=5: There are 2 = A349999(1) primes {29, 31} between 5^2 and 6^2. All intervals between squares above contain at least 3 primes.
a(2)=9: The interval [9^2, 10^2] is the last interval containing not more than 3 = A349999(2) primes {83, 89, 97}.
a(12)=80: The interval [80^2,81^2] is the last interval containing not more than 13 = A349999(12) primes {6421, ..., 6553}.
a(13)=85: The interval [85^2,86^2] is the last interval containing not more than 16 = A349999(13) primes {7229, ..., 7393}.
		

Links

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

Crossrefs

Cf. A014085, A349997, A349999.

Formula

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