Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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