login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) = x is the least number such that around x^2 (the center) the number of primes is equal to n. The radius of neighborhood is ceiling(log(x^2)).
8

%I #12 Nov 27 2017 00:44:10

%S 1,6,3,2,14,36,117,1652,9582,41361,908637,36284185

%N a(n) = x is the least number such that around x^2 (the center) the number of primes is equal to n. The radius of neighborhood is ceiling(log(x^2)).

%e n=9: a(9) = 41361, center = 1710732321, radius = 22; the nine primes in the zone are {1710732299, 1710732307, 1710732311, 1710732313, 1710732319, 1710732323, 1710732329, 1710732337, 1710732343}.

%t f[n_] := (PrimePi[n^2 + Ceiling[ Log[n^2]]] - PrimePi[n^2 - Ceiling[ Log[n^2]] - 1]); t = Table[0, {15}]; Do[a = f[n]; If[a < 15 && t[[a + 1]] == 0, t[[a + 1]] = n], {n, 10^5}] (* _Robert G. Wilson v_, Jul 14 2004 *)

%Y Cf. A096509-A096523, A096830-A096839.

%K more,nonn

%O 0,2

%A _Labos Elemer_, Jul 14 2004

%E Offset corrected and a(11) from _Donovan Johnson_, Jul 11 2010