%I #17 Mar 02 2020 18:05:05

%S 23,25,27,405,441,505,605,705,760,805,905,1005,2005,2434,3005,37600,

%T 61613,62500,67947,128891,132715,156255,5654702,6375451,9256309,

%U 9376000,17135260,379188333,382287618,393413185,486327938,492143192,524552424,668002006,734491215,824207645,906250000,930590837,964940231

%N Consider a number n with m decimal digits. The sequence lists the numbers n having the prefix of length m-1 in the middle of the decimal expansion of n^2.

%e 441 is in the sequence because 441^2 = 194481 and the prefix 44 is in the middle of the decimal expansion of 194481.

%t lst={};Do[a=IntegerDigits[n^2];b=Length[a];c=IntegerLength[(n-Mod[n,10])/10];If[EvenQ[b-c]&&FromDigits[Take[a,{(b-c)/2+1,(b+c)/2}]]==(n-Mod[n,10])/10,AppendTo[lst, n]],{n,23,5*10^6}];lst

%o (PARI) ok(n)={my(t=n^2, d=logint(n,10), b=(1+logint(t,10)-d)/2 ); d>0 && frac(b)==0 && t\10^b%10^d==n\10}

%o { for(n=1, 10^6, if(ok(n), print1(n,", "))) } \\ _Andrew Howroyd_, Mar 02 2020

%Y Cf. A000290, A242964.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, May 28 2014

%E Terms a(23) and beyond from _Andrew Howroyd_, Mar 02 2020