

A227066


Number of primes between n and 2n inclusive equals the number of primes between 2n and 3n inclusive.


0



5, 6, 15, 21, 25, 26, 28, 29, 30, 33, 35, 38, 39, 44, 47, 50, 62, 63, 65, 67, 74, 78, 80, 86, 94, 105, 108, 109, 112, 114, 153, 155, 164, 165, 170, 171, 172, 173, 174, 207, 208, 209, 215, 276, 279, 282, 283, 285, 287, 293, 294, 297, 298, 299, 504, 704, 712, 714, 1308, 1316, 1322, 1328
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OFFSET

1,1


COMMENTS

There are almost certainly no more terms. Can anyone prove this conclusively?
The analogous sequence where the number of primes between 0 and n equals the number of primes from n to 2n is finite, consisting of only 2, 4, and 10. See Ehrhart.  Charles R Greathouse IV, Jul 02 2013


LINKS

Table of n, a(n) for n=1..62.
Eugene Ehrhart, On prime numbers, Fibonacci Quarterly 26:3 (1988), pp. 271274.


FORMULA

Numbers n such that pi(3n) + pi(n1) = 2pi(2n).


EXAMPLE

4 is not in the sequence since the interval [n,2n] = [4,8] contains two primes (5 and 7), while the interval [2n,3n] = [8,12] contains only one prime (11).
6 is in the sequence since the intervals [6,12] contains two primes (7 and 11), and the interval [12,18] also contains two primes (13 and 17).


MATHEMATICA

Do[If[PrimePi[3n]+PrimePi[n1]==2*PrimePi[2n], Print[n]], {n, 4, 10^6}]


PROG

(PARI) is(n)=my(t=primepi(3*n)+primepi(n1)); t%2==0 && t==2*primepi(2*n) \\ Charles R Greathouse IV, Jul 02 2013


CROSSREFS

Sequence in context: A121847 A030533 A329634 * A115908 A247962 A241307
Adjacent sequences: A227063 A227064 A227065 * A227067 A227068 A227069


KEYWORD

nonn


AUTHOR

Zak Seidov, Jun 30 2013


STATUS

approved



