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%I #4 May 31 2014 00:54:07
%S 10,20,28,30,100,200,300,302,304,306,308,511,839,864,1000,1100,1500,
%T 1600,2000,2100,2438,2500,2600,3000,3002,3004,3006,3008,3100,5099,
%U 7046,8020,8073,9082,10000,20000,30000,30002,30004,30006,30008,30604,35000,36000
%N Consider a number n with m decimal digits. The sequence lists the numbers n having the suffix of length m-1 in the middle of the decimal expansion of n^2.
%e 511 is in the sequence because 511^2 = 261121
%e and the suffix 11 is in the middle of the decimal expansion of 261121.
%t lst={};Do[a=IntegerDigits[n^2];b=Length[a];l=IntegerLength[n]-1;c=IntegerLength[Mod[n,10^l]];If[Mod[n,10^l]==0,c=1];If[EvenQ[b-c]&&FromDigits[Take[a,{(b-c)/2+1,(b+c)/2}]]==Mod[n,10^l],AppendTo[lst,n]],{n,10,10^6}];lst
%Y Cf. A000290, A242942.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, May 28 2014