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

0, 1, 2, 9, 56, 103

Offset: 1

Author

J. Lowell, Apr 16 2014

Keywords

• nonn
• more
• hard

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

Examples

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

Crossrefs

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

Programs

Mathematica

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

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

Extensions

Zero prepended by Harvey P. Dale, Aug 16 2021