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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.
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%I #8 Dec 11 2021 10:34:52

%S 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,

%T 36,38,39,40,41,44,45,47,51,54,56,63,65,68,70,71,78,80,85,94,99,106,

%U 107,114,115,120,121,127,133,138,146,154,155,164,168,169,175,176,177

%N 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.

%C 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.

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

%H Hugo Pfoertner, <a href="/A349999/b349999.txt">Table of n, a(n) for n = 1..525</a>

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

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

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

%e See A349997 and A349998.

%Y Cf. A014085, A084597, A349997, A349998.

%Y Cf. A333846, A349996.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Dec 09 2021