

A215237


Least number k for which primepi(prime(k+1)/2)  primepi(prime(k)/2) = n.


3



1, 2, 30, 259, 429, 4612, 26466, 88110, 31545, 104071, 2775456, 14614604, 15793779, 164082567, 476853784, 495207013, 3613011290, 9032608100, 69827848342
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OFFSET

0,2


COMMENTS

See A215238 and A215239 for prime(a(n)) and the next prime.
Equivalently stated, a(n) is least k such that there are exactly n primes between prime(k)/2 and prime(k+1)/2.  Peter Munn, May 20 2019


LINKS

Table of n, a(n) for n=0..18.


EXAMPLE

For n = 2, the consecutive primes are 113 and 127; there are two primes between 56.5 and 63.5. For n = 3, the consecutive primes are 1637 and 1657; there are three primes between 818.5 and 828.5.


MATHEMATICA

t = Table[PrimePi[Prime[n+1]/2]  PrimePi[Prime[n]/2], {n, 100000}]; Flatten[Table[Position[t, n, 1, 1], {n, 0, 8}]]


CROSSREFS

Cf. A217564, A215238, A215239.
Sequence in context: A007030 A157054 A092355 * A189103 A300423 A300685
Adjacent sequences: A215234 A215235 A215236 * A215238 A215239 A215240


KEYWORD

nonn,more,hard


AUTHOR

T. D. Noe, Oct 09 2012


EXTENSIONS

a(14)a(18) from Donovan Johnson, Oct 13 2012


STATUS

approved



