A128911 Square tribonacci numbers.

0, 1, 4, 81, 3136, 10609

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

Table of n, a(n) for n=1..6.

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: A335691 A264197 A221251 * A268206 A337155 A268105

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