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

1,1

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.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..525

Formula

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

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

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

Example

See A349997 and A349998.

Crossrefs

Cf. A014085, A084597, A349997, A349998.

Cf. A333846, A349996.

Sequence in context: A114522 A283657 A053432 * A261888 A154125 A106039

Adjacent sequences: A349996 A349997 A349998 * A350000 A350001 A350002

Keyword

nonn

Author

Hugo Pfoertner, Dec 09 2021

Status

approved