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%I #34 Jun 29 2022 04:55:55
%S 1,4,9,16,35,57,93,222,427,819,1257,1270,1276,2651,5806,13673,19366,
%T 19372,27723,108857,113036,113038,115748,524856,560074,1006146,
%U 1219767,1652728,2704892,2704894,8756936,21401949,21401979,40268383,40268435,40268437,167540089,167540101
%N a(n) is the smallest number k such that A275235(k) = n.
%C Equivalently, the smallest integer k such that the number of primes between k and k+log(k)^2, exclusive, is n.
%C Up to a(37) = 167540101, the last known term, this sequence is monotonic.
%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A2, Primes connected with factorials, p. 11.
%e In the interval ]9; 9+log(9)^2[ = ]9; 13.827...[, there are two primes 11 and 13 and this is the first such interval with two primes, hence a(2) = 9.
%t f[n_] := Count[Range[n + 1, n + Log[n]^2], _?PrimeQ]; seq[len_, max_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < max, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[15, 10^4] (* _Amiram Eldar_, Jun 08 2022 *)
%Y Cf. A275235, A354842 (similar, but between k and k+log(k)).
%K nonn
%O 0,2
%A _Bernard Schott_, Jun 08 2022
%E More terms from _Amiram Eldar_, Jun 08 2022