This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A238237 #44 Jan 02 2025 12:47:22
%S A238237 81,2025,3025,9801,494209,998001,24502500,25502500,52881984,60481729,
%T A238237 99980001,6049417284,6832014336,9048004641,9999800001,101558217124,
%U A238237 108878221089,123448227904,127194229449,152344237969,213018248521,217930248900,249500250000,250500250000
%N A238237 Numbers which when chopped into two parts with equal length, added and squared result in the same number.
%C A238237 Yet another variant of the Kaprekar numbers A006886. - _N. J. A. Sloane_, Aug 06 2017
%C A238237 From _Bernard Schott_, Jan 21 2022: (Start)
%C A238237 Three subsequences:
%C A238237 -> {(10^m-1)^2, m >= 1} = A059988 \ {0}; see example 9801.
%C A238237 -> {(10^m-1)^2 * 10^(2*m) / 4, m >= 1} = A350869 \ {0}; see example 2025.
%C A238237 -> {(10^m+1)^2 * 10^(2*m) / 4, m >= 1} = A038544 \ {1}, see example 3025. (End)
%H A238237 Rémy Sigrist, <a href="/A238237/b238237.txt">Table of n, a(n) for n = 1..25000</a>
%F A238237 a(n) = A290449(n)^2. - _Bernard Schott_, Jan 20 2022
%e A238237 2025 = (20 + 25)^2, so 2025 is in the sequence.
%e A238237 3025 = (30 + 25)^2, so 3025 is in the sequence.
%e A238237 9801 = (98 + 01)^2, so 9801 is in the sequence.
%t A238237 Select[Range[600000]^2, EvenQ[len=IntegerLength[#]] && # == (Mod[#,10^(len/2)] + Floor[#/10^(len/2)])^2 &] (* _Stefano Spezia_, Jan 01 2025 *)
%o A238237 (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 A238237 Subsequence of A102766.
%Y A238237 Subsequence: A350870.
%Y A238237 Cf. A006886, A038544, A059988, A350869.
%Y A238237 For square roots see A290449.
%K A238237 nonn,base
%O A238237 1,1
%A A238237 _Arkadiusz Wesolowski_, Feb 20 2014
%E A238237 a(12)-a(24) from _Donovan Johnson_, Feb 22 2014