A354840 a(n) is the smallest number k such that A275235(k) = n.

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

Offset

0,2

Comments

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.

References

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A2, Primes connected with factorials, p. 11.

Links

Table of n, a(n) for n=0..37.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A275235, A354842 (similar, but between k and k+log(k)).

Sequence in context: A295720 A349800 A296152 * A014764 A100498 A068952

Adjacent sequences: A354837 A354838 A354839 * A354841 A354842 A354843

Keyword

nonn

Author

Bernard Schott, Jun 08 2022

Extensions

More terms from Amiram Eldar, Jun 08 2022

Status

approved