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 A215237 Least number k for which primepi(prime(k+1)/2) - primepi(prime(k)/2) = n. 3

%I

%S 1,2,30,259,429,4612,26466,88110,31545,104071,2775456,14614604,

%T 15793779,164082567,476853784,495207013,3613011290,9032608100,

%U 69827848342

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

%C See A215238 and A215239 for prime(a(n)) and the next prime.

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

%Y Cf. A217564, A215238, A215239.

%K nonn,more,hard

%O 0,2

%A _T. D. Noe_, Oct 09 2012

%E a(14)-a(18) from _Donovan Johnson_, Oct 13 2012

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Last modified October 6 04:36 EDT 2022. Contains 357261 sequences. (Running on oeis4.)