A346892 Numbers whose square starts and ends with exactly 3 identical digits.
10538, 33462, 99962, 105462, 105538, 149038, 182538, 298038, 333538, 333962, 334038, 334462, 334538, 471538, 471962, 472038, 577462, 577538, 666462, 666538, 666962, 667038, 745038, 745462, 745538, 816538, 881538, 881962, 882038, 942462, 942538, 999538, 1053962, 1054038, 1054538, 1054962
Offset: 1
Examples
10538 is a term because 10538^2 = 111049444 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. 105462 is a term because 105462^2 = 11122233444 (see A079035). 74538 is not a term because 74538^2 = 5555913444 with four starting 5's.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
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 *)
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Python
def ok(n): s = str(n*n) if len(s) < 4: return False return s[0] == s[1] == s[2] != s[3] and s[-1] == s[-2] == s[-3] != s[-4] print(list(filter(ok, range(10**6)))) # Michael S. Branicky, Aug 06 2021 -
Python
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
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