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%I #22 Jun 14 2021 11:53:30
%S 18,22,30,68,146,292,313,423,439,499,521,581,653,699,710,787,1047,
%T 1353,1425,1660,1714,2060,2174,2198,2272,2819,3019,3130,3445,3789,
%U 4366,4526,4611,4620,4624,4701,4788,4972,5261,5421,5656,6057,6106,6158,6205,6895,6927,7163,7527,7627,7733,9317,9353,10761,11092
%N Bases b for which there exists an integer y such that y^2 in base b consists of three identical digits.
%D Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428-439.
%H Giovanni Resta, <a href="/A290172/b290172.txt">Table of n, a(n) for n = 1..10000</a>
%H Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, <a href="https://arxiv.org/abs/1707.03894">The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations</a>, preprint arXiv:1707.03894 [math.NT], July 14 2017.
%e For example, for b = 18, we have y = 49, and the base-b representation of y^2 is 777.
%t r[b_] := Reduce[0 < x < b && y > 0 && y^2 == x + b x + b^2 x, {x, y}, Integers]; Reap[For[b = 2, b < 12000, b++, If[r[b] =!= False, Print[b]; Sow[b]]]][[2, 1]] (* _Jean-François Alcover_, Jul 23 2017 *)
%Y Cf. A290173, A290176, A290177, A290185.
%K nonn,base
%O 1,1
%A _Jeffrey Shallit_, Jul 23 2017