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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 6 18:41 EST 2023. Contains 367614 sequences. (Running on oeis4.)