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 A128911 Square tribonacci numbers. 1
 0, 1, 4, 81, 3136, 10609 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS These are the only square tribonacci numbers having indices < 47000. Next term, if it exists, is too large to present here. - Robert G. Wilson v, Apr 24 2007 Indices of the square tribonacci numbers: 1,4,9,15,17. The square Fibonacci numbers seem to be even rarer, namely just 1 & 144. - Robert G. Wilson v, Apr 24 2007 It is very likely that there are no further terms. - N. J. A. Sloane, Apr 25 2007 Using modular arithmetic and quadratic residues, it can be shown that there are no additional squares in the first 10^9 tribonacci numbers. - T. D. Noe, Jun 22 2007 LINKS Attila Pethö, Fifteen problems in number theory, Acta Universitatis Sapientiae. Mathematica (2010) Volume: 2, Issue: 1, page 72-83. See Problem 1. Eric Weisstein's World of Mathematics, Tribonacci Number EXAMPLE The terms 0, 1, 4, 81, 3136, 10609 are members of the sequence since their square roots are 0, 1, 2, 9, 56, 103 respectively. MATHEMATICA a = b = 0; c = 1; lst = {}; Do[{a, b, c} = {b, c, a + b + c}; If[ IntegerQ@ Sqrt@c, AppendTo[lst, c]], {n, 2, 47000}]; lst (* Robert G. Wilson v, Apr 24 2007 *) Drop[Select[LinearRecurrence[{1, 1, 1}, {0, 1, 1}, 20], IntegerQ[Sqrt[#]]&], 2] (* Harvey P. Dale, Mar 17 2017 *) CROSSREFS Intersection of A000073 and A000290. Sequence in context: A202831 A264197 A221251 * A268206 A268105 A068087 Adjacent sequences:  A128908 A128909 A128910 * A128912 A128913 A128914 KEYWORD nonn AUTHOR David A. G. Gillies, Apr 23 2007 EXTENSIONS Edited by Robert G. Wilson v, Apr 24 2007 More terms from T. D. Noe, Jun 22 2007 a(1) = 0 inserted by Felix Fröhlich, Dec 11 2019 STATUS approved

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Last modified April 1 05:33 EDT 2020. Contains 333155 sequences. (Running on oeis4.)