A104380 Smallest prime p(i) such that between 2p(i) and 2p(i+1) there exist n primes.

59, 2, 5, 31, 89, 509, 113, 1129, 1951, 7253, 19609, 16141, 13339, 28229, 1327, 281431, 396733, 1122287, 461717, 370261, 2010733, 492113, 3279841, 14246971, 3117299, 5826001, 20831323, 47326693, 60487759, 189695659, 191912783, 1301171033, 2044207843, 3129752191, 476956933, 836806669, 2433630109

Offset

0,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..53

Example

a(0)=59 because between 2*59=118 and 2*61=122 there are no primes and 59 is the least prime with this characteristic.
a(4)=89 because between 2*89=178 and 2*97=194 there are 4 primes, namely 179, 181, 191 and 193.

Mathematica

f[n_] := PrimePi[2Prime[n + 1]] - PrimePi[2Prime[n]]; t = Table[0, {30}]; Do[a = f[n]; If[t[[a + 1]] == 0, t[[a + 1]] = Prime[n]], {n, 2500000}]; t

Prog

(PARI) ct(a, b)=sum(k=a, b, isprime(k))
a(n)=my(p=2); forprime(q=3, , if(ct(2*p+1, 2*q-1)==n, return(p)); p=q) \\ Charles R Greathouse IV, Nov 05 2017

Crossrefs

Cf. A060756, A102820, A215238.

Sequence in context: A116103 A116115 A230852 * A051321 A235774 A088665

Adjacent sequences: A104377 A104378 A104379 * A104381 A104382 A104383

Keyword

nonn

Author

Ali A. Tanara (tanara(AT)khayam.ut.ac.ir) and Robert G. Wilson v, Mar 03 2005

Extensions

a(27)-a(36) from Charles R Greathouse IV, Nov 05 2017

Status

approved