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%I #37 Jan 26 2022 08:32:49
%S 81,2025,3025,9801,494209,998001,24502500,25502500,52881984,60481729,
%T 99980001,6049417284,6832014336,9048004641,9999800001,101558217124,
%U 108878221089,123448227904,127194229449,152344237969,213018248521,217930248900,249500250000,250500250000
%N Numbers which when chopped into two parts with equal length, added and squared result in the same number.
%C Yet another variant of the Kaprekar numbers A006886. - _N. J. A. Sloane_, Aug 06 2017
%C From _Bernard Schott_, Jan 21 2022: (Start)
%C Three subsequences:
%C -> {(10^m-1)^2, m >= 1} = A059988 \ {0}; see example 9801.
%C -> {(10^m-1)^2 * 10^(2*m) / 4, m >= 1} = A350869 \ {0}; see example 2025.
%C -> {(10^m+1)^2 * 10^(2*m) / 4, m >= 1} = A038544 \ {1}, see example 3025. (End)
%H Rémy Sigrist, <a href="/A238237/b238237.txt">Table of n, a(n) for n = 1..25000</a>
%F a(n) = A290449(n)^2. - _Bernard Schott_, Jan 20 2022
%e 2025 = (20 + 25)^2, so 2025 is in the sequence.
%e 3025 = (30 + 25)^2, so 3025 is in the sequence.
%e 9801 = (98 + 01)^2, so 9801 is in the sequence.
%o (PARI) forstep(m=1, 7, 2, p=10^((m+1)/2); for(n=10^m, 10^(m+1)-1, d=lift(Mod(n, p)); if(((n-d)/p+d)^2==n, print1(n, ", "))));
%Y Subsequence of A102766.
%Y Subsequence: A350870.
%Y Cf. A006886, A038544, A059988, A350869.
%Y For square roots see A290449.
%K nonn,base
%O 1,1
%A _Arkadiusz Wesolowski_, Feb 20 2014
%E a(12)-a(24) from _Donovan Johnson_, Feb 22 2014
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