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Numbers whose squares have the first three digits the same as the next three digits.
2

%I #15 Jan 10 2023 20:26:40

%S 1429,1537,1692,1823,2001,2312,2467,2729,2858,3148,3242,3635,3849,

%T 4002,4541,4552,5851,6003,6216,6296,6375,7145,7152,7159,7698,8004,

%U 9093,9104,9235,9444,10005,10154,12006,12335,13645,14007,14290,14325,15272,15370,16008,16531

%N Numbers whose squares have the first three digits the same as the next three digits.

%H Alois P. Heinz, <a href="/A353080/b353080.txt">Table of n, a(n) for n = 1..10000</a>

%e 1429^2 = 2042041 and 1537^2 = 2362369. Thus, 1429 and 1537 are both in this sequence.

%p q:= n-> (s-> is(s[1..3]=s[4..6]))(""||(n^2)):

%p select(q, [$317..17000])[]; # _Alois P. Heinz_, Apr 22 2022

%t Select[Range[317, 20000], Take[IntegerDigits[#^2], {1, 3}] == Take[IntegerDigits[#^2], {4, 6}] &]

%o (Python)

%o def ok(n): s = str(n**2); return len(s) > 5 and s[:3] == s[3:6]

%o print([k for k in range(20000) if ok(k)]) # _Michael S. Branicky_, Apr 22 2022

%Y Cf. A123912, A353081.

%K nonn,base

%O 1,1

%A _Tanya Khovanova_, Apr 22 2022