A127441 Numbers n such that between n and n+sqrt(n) there are no primes.

3, 7, 8, 13, 23, 24, 31, 113, 114, 115, 116

Offset: 1

Author

Artur Jasinski, Jan 14 2007

Keywords

• nonn
• more

Comments

If Oppermann's conjecture is true, then all terms are nonsquares. Data from A002386 and A005250 show that a(12) > 6787988999657777797 if it exists. Most likely there are no further terms. - Chai Wah Wu, Mar 08 2019

Links

• Wikipedia, Oppermann's conjecture

Crossrefs

Cf. A000720, A002386, A005250, A028392.

Programs

Mathematica

a = {}; Do[If[PrimePi[x + x^(1/2)] - PrimePi[x] == 0, AppendTo[a, x]], {x, 1, 249900000000000}]; a

PARI

isok(n) = primepi(n+sqrtint(n)) == primepi(n); \\ Michel Marcus, Nov 07 2013