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

Author

Bernard Schott, Aug 06 2021

Keywords

• nonn
• base

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

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

Intersection of A039685 and A346891.

Cf. A346774 (similar, with 2 identical digits).

A348832 is a subsequence.

Programs

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 *)

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