A215237 Least number k for which primepi(prime(k+1)/2) - primepi(prime(k)/2) = n.

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

Offset: 0

Author

T. D. Noe, Oct 09 2012

Keywords

• nonn
• more
• hard

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

Examples

			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.
		

Crossrefs

Cf. A217564, A215238, A215239.

Programs

Mathematica

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

Extensions

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