A380522 Primes p such that between p and the previous prime there exist 2 distinct integers which are a square and a cube, respectively.

11, 29, 127, 32771, 79531, 97367

Offset: 1

Author

Zhining Yang, Jan 26 2025

Keywords

• nonn
• hard
• more

Comments

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

Examples

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

Crossrefs

Cf. A053706, A380521, A380523.

Programs

Mathematica

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