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%I #24 Jul 30 2021 08:44:25
%S 9,49,249,1249,18751,218751,781249,24218751,74218751,1425781249,
%T 13574218751,163574218751,163574218751,19836425781249,19836425781249,
%U 2480163574218751,12519836425781249,12519836425781249,487480163574218751,15487480163574218751,215487480163574218751,215487480163574218751
%N Smallest number m > 1 such that m^2 == 1 (mod 10^n).
%C a(n) > 10^floor(n/2).
%C All terms have last digit 1 or 9.
%C Squares of terms are listed in A085877.
%C Decimal representation of each term is formed by the reverse concatenation of initial terms of either A063006 or A091661.
%C Except for 3, there are no solutions for n>1 and m^2 == -1 (mod 10^n). See comment in A063006 under extensions. - _Robert G. Wilson v_, Jan 26 2013
%C If a(n)<(10^n)/2 then (10^n-a(n))^2 is also congruent (modulo 10^n), its just not the least. - _Robert G. Wilson v_, Jan 26 2013
%H Max Alekseyev, <a href="/A181539/b181539.txt">Table of n, a(n) for n = 1..1000</a>
%e 1249^2 = 1560001 == 1 (mod 10^4), and there is no smaller m > 1 such that m^2 == 1 (mod 10^4). Hence a(4) = 1249.
%Y Cf. A085610, A181607. [From _R. J. Mathar_, Oct 30 2010]
%K nonn
%O 1,1
%A Kevin Batista (kevin762401(AT)yahoo.com), Oct 29 2010
%E a(2) through a(4), a(7) through a(11) corrected, comment added, example replaced by _Klaus Brockhaus_, Nov 01 2010
%E Edited by _N. J. A. Sloane_, Oct 29 2010, Nov 09 2010
%E Definition to avoid the constant sequence a(n)=1 constrained by _R. J. Mathar_, Nov 18 2010
%E a(1) corrected, terms a(13) onward added by _Max Alekseyev_, Dec 10 2012
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