A353081 Numbers whose squares have the first two digits the same as the next two digits.
201, 264, 402, 482, 603, 689, 772, 804, 932, 964, 1005, 1101, 1146, 1231, 1557, 1798, 1907, 2010, 2035, 2084, 2132, 2202, 2357, 2582, 2640, 2659, 2678, 2734, 2878, 3015, 3114, 3179, 3334, 3482, 3624, 3761, 3893, 4020, 4021, 4144, 4264, 4381, 4495, 4606, 4714, 4820, 4924
Offset: 1
Programs
-
Maple
q:= n-> (s-> is(s[1..2]=s[3..4]))(""||(n^2)): select(q, [$32..10000])[]; # Alois P. Heinz, Apr 22 2022 -
Mathematica
Select[Range[32, 5000], Take[IntegerDigits[#^2], {1, 2}] == Take[IntegerDigits[#^2], {3, 4}] &] -
PARI
do(n)=my(v=List()); for(a=1,9, for(b=0,9, my(N=10^(n-4), t=(1010*a+101*b)*N-1); for(k=sqrtint(t)+1,sqrtint(t+N), listput(v,k)))); Vec(v) \\ finds terms corresponding to n-digit squares; Charles R Greathouse IV, Apr 24 2022
-
Python
def ok(n): s = str(n**2); return len(s) > 3 and s[:2] == s[2:4] print([k for k in range(5000) if ok(k)]) # Michael S. Branicky, Apr 22 2022
Formula
201^2 = 40401 and 264^2 = 69696. Thus, both 201 and 264 are in this sequence.