A199496 Good examples of a tightened Hall's conjecture: integers x such that 0 < x^3 - y^2 < sqrt(x) for some integer y.

367806, 939787, 952764389446, 12438517260105, 35495694227489, 5853886516781223, 23415546067124892, 38115991067861271, 322001299796379844, 9870884617163518770, 42532374580189966073, 51698891432429706382, 601724682280310364065

Offset: 1

Author

Artur Jasinski, Nov 07 2011

Keywords

• nonn
• hard

Comments

This sequence is the subset of x in A078933 such that x^3-(round(sqrt(x^3)))^2 is positive. This means the definition here does not take absolute values of x^3-y^2 as A078933 does.

Crossrefs

Cf. A078933.