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A317027
Perfect powers that appear more than once in the Catalan triangle.
1
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
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
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(9)-a(16) from Giovanni Resta, Jul 29 2018
STATUS
approved