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.
101 is not a term since the two digits 1 are separated by the 0. 233 is a term since the digits 2 and 3 are grouped, and it is prime.
81 is not a term since in 81^2 = 6561, the two 6's are separated by the 5. 88 is a term since in 88^2 = 7744, the 7 and 4 are grouped.
filter:= proc(n) local L,i,v,V;
L:= convert(n^2,base,10);
for i from 1 to nops(L) do
v:= L[i];
if not assigned(V[v]) then V[v]:= i
elif V[v] < i-1 then return false
else V[v]:= i
fi
od;
true
end proc:
select(filter, [$0..100]); # Robert Israel, Nov 08 2023
10609 is a term since the two digits 0 are separated by the 6. 7744 is not a term since all the digits 7 and 4 are grouped.
81 is not a term because in 81^3 = 531441 the two digits 1 are separated by the two 4's. 15 is a term because in 15^3 = 3375 the digits 3, 7 and 5 are grouped.
The cube 300763 is a term since the digits 3 are separated by the substring 0076. The cube 97336 is not a term since its 3-digits are grouped.