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A354840
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a(n) is the smallest number k such that A275235(k) = n.
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1
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1, 4, 9, 16, 35, 57, 93, 222, 427, 819, 1257, 1270, 1276, 2651, 5806, 13673, 19366, 19372, 27723, 108857, 113036, 113038, 115748, 524856, 560074, 1006146, 1219767, 1652728, 2704892, 2704894, 8756936, 21401949, 21401979, 40268383, 40268435, 40268437, 167540089, 167540101
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OFFSET
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0,2
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COMMENTS
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Equivalently, the smallest integer k such that the number of primes between k and k+log(k)^2, exclusive, is n.
Up to a(37) = 167540101, the last known term, this sequence is monotonic.
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REFERENCES
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Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A2, Primes connected with factorials, p. 11.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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