A288854 - OEIS

%I #23 Jun 19 2017 12:03:21

%S 25,625,5625,75625,275625

%N The unique longest sequence of squares where each number (after the first) is obtained by prefixing a single digit to its predecessor.

%C This chain with five squares is the longest which exists in this context, there is no such sequence of length >= 6.

%C There are also only four chains of maximal length 4 with:

%C -> 25, 225, 1225, 81225. These four squares are the first terms of A061839.

%C -> 25, 225, 4225, 34225.

%C -> 25, 225, 7225, 27225. These four squares are the first terms of A191486.

%C -> 25, 625, 5625, 15625.

%C There are also only three chains of maximal length 3 with:

%C -> 3025, 93025, 893025.

%C -> 30625, 330625, 3330625.

%C -> 50625, 950625, 4950625.

%C See Crux Mathematicorum links.

%H L. Csirmaz, <a href="https://cms.math.ca/crux/backfile/Crux_v7n09_Nov.pdf">Problem 526, solution</a>, Crux Mathematicorum, page 280, Vol.7, Nov. 81.

%H Friend H. Kierstead, Jr., <a href="https://cms.math.ca/crux/backfile/Crux_v7n03_Mar.pdf">Problem 526, partial solution</a>, Crux Mathematicorum, page 87, Vol.7, Mar. 81.

%e 25 = 5^2; 625 = 25^2; 5625 = 75^2; 75625 = 275^2; 275625 = 525^2.

%Y Cf. A061839, A191486.

%K nonn,fini,full,base

%O 1,1

%A _Bernard Schott_, Jun 18 2017