A380405 Squares k such that there are no primes between k and the nearest cube that is not k.

9, 25, 121, 32761, 79524, 97344

Offset: 1

Author

Zhining Yang, Jan 26 2025

Keywords

• nonn
• hard
• more

Comments

There are no other terms < 2*10^30.

Examples

			121 is a term because it is a square and there are no primes between 123 and 125, its nearest cube.
		

Crossrefs

Cf. A053706, A380521, A380522, A380523, A078933.

Programs

Mathematica

b[n_] := If[IntegerQ@Sqrt@n, 0, p = NextPrime[n^3];
  q = Ceiling[Sqrt[NextPrime[p, -1]]];  If[q^2 >= p, 0, q]];
 Select[Array[b@# &, 1000], # > 0 &]^2