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

1,1

Links

Table of n, a(n) for n=1..47.

Formula

201^2 = 40401 and 264^2 = 69696. Thus, both 201 and 264 are in this sequence.

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}] &]

Prog

(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
(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

Crossrefs

Cf. A123912, A353080.

Sequence in context: A296022 A338591 A347887 * A259768 A076192 A157956

Adjacent sequences: A353078 A353079 A353080 * A353082 A353083 A353084

Keyword

nonn,base,easy

Author

Tanya Khovanova, Apr 22 2022

Status

approved