A354842 a(n) is the smallest number k such that A354841(k) = n.

1, 4, 28, 1276, 9430, 463446, 24786396, 1340301868

Offset: 0

Author

Bernard Schott, Jun 24 2022

Keywords

• nonn
• more

Comments

Equivalently, the smallest integer k such that the number of primes between k and k+log(k), exclusive, is n.

Examples

			In the interval ]28; 28+log(28)[ = ]28; 31.332...[, there are two primes 29 and 31 and this is the first such interval with 2 primes, hence a(2) = 28.
		

Crossrefs

Cf. A354840 (similar, but between k and k+log(k)^2), A354841.

Programs

Mathematica

seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = Count[Range[n + 1, n + Log[n]], ?PrimeQ] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[5, 10^5] (* _Amiram Eldar, Jun 25 2022 *)

Extensions

a(3)-a(5) from Alois P. Heinz, Jun 25 2022

a(6) from Amiram Eldar, Jun 25 2022

a(7) from David Consiglio, Jr., Jun 29 2022