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Integers whose squares are in A000073 (tribonacci numbers).
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%I #41 Jun 10 2022 06:16:46

%S 0,1,2,9,56,103

%N Integers whose squares are in A000073 (tribonacci numbers).

%C a(6) > 10^7. - _Tom Edgar_, Apr 26 2014

%C Is this sequence finite?

%C No more terms < 10^19300. I conjecture that the sequence is finite. - _Manfred Scheucher_, Aug 17 2015

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

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

%o (Sage)

%o def tribs():

%o a,b,c = 0,0,1

%o while True:

%o yield a

%o a,b,c = b,c,a+b+c

%o for n in tribs():

%o m = sqrt(n)

%o if m.is_integer():

%o print(m) # _Manfred Scheucher_, Aug 17 2015

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

%K nonn,more,hard

%O 1,3

%A _J. Lowell_, Apr 16 2014

%E Zero prepended by _Harvey P. Dale_, Aug 16 2021