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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A284890 A051214 A256722 * 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

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)