A380521 Primes p such that between p and the next prime there exist 2 distinct integers which are a square and a cube, respectively.

7, 23, 113, 32749, 79493, 97327

Offset: 1

Author

Zhining Yang, Jan 26 2025

Keywords

• nonn
• hard
• more

Comments

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

Examples

			113 is a term because between prime 113 and next prime 127 there exists a square 121 and a cube 125.
		

Crossrefs

Cf. A053706, A380522, A380523.

Programs

Mathematica

b[n_] := If[IntegerQ@Sqrt@n, 0, p = NextPrime[n^3, -1];
  If[Floor[Sqrt[NextPrime[p]]]^2 <= p, 0, p]]; Select[Array[b@# &, 100], # > 0 &]