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

1,1

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

Table of n, a(n) for n=1..16.

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.

Sequence in context: A286524 A057901 A320676 * A020254 A124396 A020281

Adjacent sequences: A317024 A317025 A317026 * A317028 A317029 A317030

Keyword

nonn,more

Author

Eric Jovinelly, Eugene Fiorini, Jul 19 2018

Extensions

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

Status

approved