A349997 Numbers k such that the number of primes in any interval [j^2,(j+1)^2], j>k, is not less than the number of primes in the interval [k^2,(k+1)^2].

1, 7, 11, 17, 18, 26, 27, 32, 46, 50, 56, 58, 85, 88, 92, 137, 143, 145, 152, 157, 178, 188, 194, 200, 201, 208, 225, 232, 253, 263, 279, 297, 327, 331, 339, 360, 433, 451, 485, 506, 536, 541, 607, 696, 708, 717, 768, 799, 801, 806, 904, 913, 1015, 1059, 1110, 1111

Offset

1,2

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.

Links

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

Formula

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

Example

a(1)=1: the interval [1^2, 2^2] contains A349999(1)=2 primes {2, 3}, and no later interval contains less than 2 primes.
a(2)=7: the interval [7^2, 8^2] contains A349999(2)=3 primes {53, 59, 61}, and no later interval contains less than 3 primes.
a(12)=58: the interval [58^2, 59^2] contains A349999(12)=13 primes {3371, ..., 3469}, and no later interval contains less than 13 primes.
a(13)=85: the interval [85^2, 86^2] contains A349999(13)=16 primes {7229, ..., 7393}, and no later interval contains less than 16 primes.

Crossrefs

Cf. A014085, A349998, A349999.

Sequence in context: A131626 A086762 A296305 * A076045 A101618 A147956

Adjacent sequences: A349994 A349995 A349996 * A349998 A349999 A350000

Keyword

nonn

Author

Hugo Pfoertner, Dec 09 2021

Status

approved