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A271383 Smallest k such that there are exactly n primes between k*(k-1) 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 (list; graph; refs; listen; history; text; internal format)
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*(38-1) = 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*(k-1)))!=n || (primepi(k*(k+1))-primepi(k^2))!=n, k++); k

CROSSREFS

Sequence in context: A156245 A247783 A096274 * A193666 A196024 A037382

Adjacent sequences:  A271380 A271381 A271382 * A271384 A271385 A271386

KEYWORD

nonn,more

AUTHOR

Felix Fröhlich, Apr 07 2016

STATUS

approved

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Last modified February 24 21:22 EST 2018. Contains 299628 sequences. (Running on oeis4.)