A317027 Perfect powers that appear more than once in the Catalan triangle.

9, 27, 324, 8000, 11025, 374544, 12723489, 432224100, 14682895929, 498786237504, 16944049179225, 575598885856164, 19553418069930369, 664240615491776400, 22564627508650467249, 766533094678624110084

Offset: 1

Author

Eric Jovinelly, Eugene Fiorini, Jul 19 2018

Keywords

• nonn
• more

Comments

Since every integer appears exactly once in the first column of the Catalan triangle, this sequence lists perfect powers that appear in any other column of the triangle. Pell's equation can be used to prove that infinitely many perfect squares appear in this sequence.

Links

• Nathaniel Benjamin, Grant Fickes, Eugene Fiorini, Edgar Jaramillo Rodriguez, Eric Jovinelly, Tony W. H. Wong, Primes and Perfect Powers in the Catalan Triangle, J. Int. Seq., Vol. 22 (2019), Article 19.7.6.
• Eric Jovinelly, Python program

Crossrefs

Cf. A009766.

Subsequence of A275586.

Extensions

a(9)-a(16) from Giovanni Resta, Jul 29 2018