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A346942 Numbers whose square starts and ends with exactly 4 identical digits.

%I A346942 #33 Oct 02 2021 13:13:34
%S A346942 235700,258200,333400,471400,577400,666700,816500,881900,942800,
%T A346942 1054200,1054300,1054400,1054500,1490700,1490800,1490900,1825700,
%U A346942 1825800,1825900,2108100,2108200,2108300,2357100,2581900,2788800,2788900,2981300,2981400,3162200,3333200,3333300
%N A346942 Numbers whose square starts and ends with exactly 4 identical digits.
%C A346942 Terms are equal to 100 times the primitive terms of A346940, those that have no trailing zero in decimal representation, hence all terms end with exactly 00.
%H A346942 Chai Wah Wu, <a href="/A346942/b346942.txt">Table of n, a(n) for n = 1..10000</a>
%e A346942 258200 is a term because 258200^2 = 66667240000 starts with four 6's and ends with four 0's.
%e A346942 3334700 is not a term because 3334700^2 = 1111155560000 starts with five 1's (and ends with four 0's).
%t A346942 q[n_] := SameQ @@ (d = IntegerDigits[n^2])[[1 ;; 4]] && d[[5]] != d[[1]] && SameQ @@ d[[-4 ;; -1]] && d[[-5]] != d[[-1]]; Select[Range[10000, 3333300], q] (* _Amiram Eldar_, Aug 08 2021 *)
%o A346942 (Python)
%o A346942 def ok(n):
%o A346942   s = str(n*n)
%o A346942   return len(s) > 4 and s[0] == s[1] == s[2] == s[3] != s[4] and s[-1] == s[-2] == s[-3] == s[-4] != s[-5]
%o A346942 print(list(filter(ok, range(3333333)))) # _Michael S. Branicky_, Aug 08 2021
%o A346942 (Python)
%o A346942 A346942_list = [100*n for n in range(99,10**6) if n % 10 and (lambda x:x[0]==x[1]==x[2]==x[3]!=x[4])(str(n**2))] # _Chai Wah Wu_, Oct 02 2021
%Y A346942 Numbers whose square '....' with exactly k identical digits:
%Y A346942   ---------------------------------------------------------------------------
%Y A346942   |    k  \'....'|    starts     |       ends         |   starts and ends   |
%Y A346942   ---------------------------------------------------------------------------
%Y A346942   |     k = 2    |    A346812    |      A346678       |       A346774       |
%Y A346942   |     k = 3    |    A346891    |      A039685       |       A346892       |
%Y A346942   |     k = 4    |    A346940    |    100*A067251     |    this sequence    |
%Y A346942   ---------------------------------------------------------------------------
%Y A346942 Cf. A346926.
%K A346942 nonn,base
%O A346942 1,1
%A A346942 _Bernard Schott_, Aug 08 2021