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COMMENTS
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This chain with five squares is the longest which exists in this context, there is no such sequence of length >= 6.
There are also only four chains of maximal length 4 with:
-> 25, 225, 1225, 81225. These four squares are the first terms of A061839.
-> 25, 225, 4225, 34225.
-> 25, 225, 7225, 27225. These four squares are the first terms of A191486.
-> 25, 625, 5625, 15625.
There are also only three chains of maximal length 3 with:
-> 3025, 93025, 893025.
-> 30625, 330625, 3330625.
-> 50625, 950625, 4950625.
See Crux Mathematicorum links.
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LINKS
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Table of n, a(n) for n=1..5.
L. Csirmaz, Problem 526, solution, Crux Mathematicorum, page 280, Vol.7, Nov. 81.
Friend H. Kierstead, Jr., Problem 526, partial solution, Crux Mathematicorum, page 87, Vol.7, Mar. 81.
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