A349999 - OEIS

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

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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.