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A346892 Numbers whose square starts and ends with exactly 3 identical digits. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The terminal digits of the square of terms are necessarily 444.
The last 3 digits of terms are either 038, 462, 538 or 962. - Chai Wah Wu, Oct 02 2021
LINKS
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
Intersection of A039685 and A346891.
Cf. A346774 (similar, with 2 identical digits).
A348832 is a subsequence.
Sequence in context: A120500 A157487 A203666 * A119866 A292703 A065319
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Aug 06 2021
STATUS
approved

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Last modified April 18 03:33 EDT 2024. Contains 371767 sequences. (Running on oeis4.)