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A346892 Numbers whose square starts and ends with exactly 3 identical digits.

%I A346892 #27 May 06 2022 13:13:51
%S A346892 10538,33462,99962,105462,105538,149038,182538,298038,333538,333962,
%T A346892 334038,334462,334538,471538,471962,472038,577462,577538,666462,
%U A346892 666538,666962,667038,745038,745462,745538,816538,881538,881962,882038,942462,942538,999538,1053962,1054038,1054538,1054962
%N A346892 Numbers whose square starts and ends with exactly 3 identical digits.
%C A346892 The terminal digits of the square of terms are necessarily 444.
%C A346892 The last 3 digits of terms are either 038, 462, 538 or 962. - _Chai Wah Wu_, Oct 02 2021
%H A346892 Chai Wah Wu, <a href="/A346892/b346892.txt">Table of n, a(n) for n = 1..10000</a>
%e A346892 10538 is a term because 10538^2 = 111049444
%e A346892 666462 = A348832(1) is a term because 666462^2 = 444171597444, the smallest square that starts with exactly three 4's and ends also with three 4's.
%e A346892 105462 is a term because 105462^2 = 11122233444 (see A079035).
%e A346892 74538 is not a term because 74538^2 = 5555913444 with four starting 5's.
%t A346892 Select[Range[10^3, 10^6], (d = IntegerDigits[#^2])[[1]] == d[[2]] == d[[3]] != d[[4]] && d[[-1]] == d[[-2]] == d[[-3]] != d[[-4]] &] (* _Amiram Eldar_, Aug 06 2021 *)
%o A346892 (Python)
%o A346892 def ok(n):
%o A346892     s = str(n*n)
%o A346892     if len(s) < 4: return False
%o A346892     return s[0] == s[1] == s[2] != s[3] and s[-1] == s[-2] == s[-3] != s[-4]
%o A346892 print(list(filter(ok, range(10**6)))) # _Michael S. Branicky_, Aug 06 2021
%o A346892 (Python)
%o A346892 A346892_list = [1000*n+d for n in range(10**6) for d in [38,462,538,962] if (lambda x:x[0]==x[1]==x[2]!=x[3])(str((1000*n+d)**2))] # _Chai Wah Wu_, Oct 02 2021
%Y A346892 Intersection of A039685 and A346891.
%Y A346892 Cf. A346774 (similar, with 2 identical digits).
%Y A346892 A348832 is a subsequence.
%K A346892 nonn,base
%O A346892 1,1
%A A346892 _Bernard Schott_, Aug 06 2021