

A271383


Smallest k such that there are exactly n primes between k*(k1) and k^2 and exactly n primes between k^2 and k*(k+1).


0



2, 8, 13, 21, 32, 38, 46, 60, 85, 74, 102, 111
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OFFSET

1,1


COMMENTS

Does k exist for every n?


LINKS

Table of n, a(n) for n=1..12.
Wikipedia, Oppermann's conjecture.


EXAMPLE

For n = 6: 38*(381) = 1406, 38^2 = 1444 and 38*(38+1) = 1482. A000720(1444)  A000720(1406) = 6 and A000720(1482)  A000720(1444) = 6. Since 38 is the smallest k where the number of primes in both intervals is 6, a(6) = 38.


MATHEMATICA

Table[SelectFirst[Range[10^3], And[PrimePi[#^2]  PrimePi[# (#  1)] == n, PrimePi[# (# + 1)]  PrimePi[#^2] == n] &], {n, 30}] /. k_ /; MissingQ@ k > 0 (* Michael De Vlieger, Apr 09 2016, Version 10.2 *)


PROG

(PARI) a(n) = my(k=1); while((primepi(k^2)primepi(k*(k1)))!=n  (primepi(k*(k+1))primepi(k^2))!=n, k++); k


CROSSREFS

Sequence in context: A247783 A096274 A305879 * A193666 A196024 A037382
Adjacent sequences: A271380 A271381 A271382 * A271384 A271385 A271386


KEYWORD

nonn,more


AUTHOR

Felix FrÃ¶hlich, Apr 07 2016


STATUS

approved



