This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A215237 #15 May 25 2019 17:24:23
%S A215237 1,2,30,259,429,4612,26466,88110,31545,104071,2775456,14614604,
%T A215237 15793779,164082567,476853784,495207013,3613011290,9032608100,
%U A215237 69827848342
%N A215237 Least number k for which primepi(prime(k+1)/2) - primepi(prime(k)/2) = n.
%C A215237 See A215238 and A215239 for prime(a(n)) and the next prime.
%C A215237 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
%e A215237 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.
%t A215237 t = Table[PrimePi[Prime[n+1]/2] - PrimePi[Prime[n]/2], {n, 100000}]; Flatten[Table[Position[t, n, 1, 1], {n, 0, 8}]]
%Y A215237 Cf. A217564, A215238, A215239.
%K A215237 nonn,more,hard
%O A215237 0,2
%A A215237 _T. D. Noe_, Oct 09 2012
%E A215237 a(14)-a(18) from _Donovan Johnson_, Oct 13 2012