A127459 Prime numbers n such that there are no primes between n and n+n^(1/3).

3, 5, 7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 73, 83, 89, 113, 131, 139, 151, 157, 167, 173, 181, 199, 211, 241, 283, 293, 317, 337, 359, 389, 401, 409, 421, 449, 467, 479, 491, 509, 523, 547, 577, 619, 631, 661, 691, 709, 773, 787, 797, 811, 829, 839, 863, 887

Offset: 1

Author

Artur Jasinski, Jan 15 2007

Keywords

• nonn

Comments

Subsequence of A127458. - Michel Marcus, Nov 06 2013

Links

• Donovan Johnson, Table of n, a(n) for n = 1..396 (probably complete)

Crossrefs

Cf. A127441, A127458.

Programs

Mathematica

a = {}; Do[If[(PrimePi[x + x^(1/3)] - PrimePi[x] == 0) && (PrimeQ[x]), AppendTo[a, x]], {x, 1, 20000}]; a
Select[Prime[Range[200]],PrimePi[#]==PrimePi[#+Surd[#,3]]&] (* Harvey P. Dale, Sep 12 2017 *)

PARI

is(n)=isprime(n) && (nextprime(n+1)-n)^3>n \\ Charles R Greathouse IV, Dec 09 2014