A192391 Numbers k such that the number of primes in the open interval (k^2 - k, k^2) is equal to the number of primes in the open interval (k^2, k^2 + k).

1, 2, 3, 5, 8, 9, 12, 13, 14, 20, 21, 24, 26, 28, 30, 32, 34, 35, 38, 39, 46, 48, 51, 53, 55, 60, 67, 72, 74, 83, 85, 94, 102, 107, 111, 135, 154, 161, 162, 192, 200, 206, 221, 237, 254, 258, 277, 280, 283, 288, 301, 314

Offset

1,2

Links

Table of n, a(n) for n=1..52.

Example

a(1)=1 because there are no primes in the interval (1^2-1, 1^2) = (0, 1) and no primes in the interval (1^2, 1^2+1) = (1, 2).
a(2)=2 because there is 1 prime in the interval (2^2-2, 2^2) = (2, 4) and one prime in the interval (2^2, 2^2+2) = (4, 6).

Maple

isA192391 := proc(n) numtheory[pi](n^2-1)-numtheory[pi](n^2-n) = numtheory[pi](n^2+n-1)-numtheory[pi](n^2-1) ; end proc:
for n from 1 to 600 do if isA192391(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Jul 08 2011

Mathematica

Select[Range[500], PrimePi[#^2] - PrimePi[#^2 - #] == PrimePi[#^2 + #] - PrimePi[#^2] &] (* Alonso del Arte, Jun 29 2011 *)

Crossrefs

Cf. A000040.

Sequence in context: A256722 A364926 A363097 * A013634 A133484 A181155

Adjacent sequences: A192388 A192389 A192390 * A192392 A192393 A192394

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 29 2011

Extensions

32 inserted and a few terms beyond 51 added by Alonso del Arte, Jun 29 2011

Status

approved