A240562 Integers whose squares are in A000073 (tribonacci numbers).

0, 1, 2, 9, 56, 103

Offset

1,3

Comments

a(6) > 10^7. - Tom Edgar, Apr 26 2014

Is this sequence finite?

No more terms < 10^19300. I conjecture that the sequence is finite. - Manfred Scheucher, Aug 17 2015

Links

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

Example

9^2 = 81 is in the tribonacci sequence, so 9 is a term.

Mathematica

Select[Sqrt[#]&/@LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 200], IntegerQ]// Union (* Harvey P. Dale, Aug 16 2021 *)

Prog

(Sage)
def tribs():
    a, b, c = 0, 0, 1
    while True:
        yield a
        a, b, c = b, c, a+b+c
for n in tribs():
    m = sqrt(n)
    if m.is_integer():
        print(m) # Manfred Scheucher, Aug 17 2015

Crossrefs

Cf. A000073 (tribonacci numbers), A128911 (the corresponding squares).

Sequence in context: A241457 A229208 A154749 * A091108 A179405 A081004

Adjacent sequences: A240559 A240560 A240561 * A240563 A240564 A240565

Keyword

nonn,more,hard

Author

J. Lowell, Apr 16 2014

Extensions

Zero prepended by Harvey P. Dale, Aug 16 2021

Status

approved