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%I #25 Jun 15 2021 01:30:09
%S 6,2,615,84,119973,4,3,23620,36363636364,6,24766945690,17928148,915,4,
%T 86808207405692007605,6,130,10,2667,95530227420606,10623969116570,12,
%U 5,343872950627253606,9,14,59239353339085,8130
%N a(n)^2 is the least square base-n doublet (base-n representation is the concatenation of 2 identical strings).
%C The identical strings must contain at least one nonzero digit, so that a(n) > 0. - _Alonso del Arte_, Jun 20 2018
%C In Bridy et al. it is shown how to construct an example (although not necessarily the least example) for each integer base n >= 2. - _Jeffrey Shallit_, Jun 14 2021
%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.
%D David Wells, "The Penguin Dictionary of Curious and Interesting Numbers", Revised Edition 1997, p. 189.
%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.
%H A. Ottens, <a href="https://web.archive.org/web/20041013050849/http://rec-puzzles.org:80/sol.pl/arithmetic/digits/squares/three.digits">The arithmetic-digits-squares-three.digits problem</a>
%e The first few squares in binary are 1, 100, 1001, 10000, 11001, 100100. Thus we see that 100100, which is 36 in decimal, the square of 6, is the first square which is the concatenation of two identical bit patterns, and therefore a(2) = 6.
%Y Cf. A020340, A054214, A054215, A054216, A030465, A030466, A030467.
%K base,nonn
%O 2,1
%A _David W. Wilson_
%E Name slightly adjusted by _Alonso del Arte_, Jun 20 2018
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