A346774 Numbers whose square starts and ends with exactly 2 identical digits.

88, 150, 210, 212, 338, 340, 470, 580, 670, 880, 940, 1050, 1060, 1062, 1070, 1080, 1088, 1090, 1488, 1510, 1512, 1820, 1830, 1838, 1840, 2110, 2112, 2120, 2350, 2360, 2362, 2570, 2580, 2588, 2780, 2790, 2970, 3150, 3160, 3320, 3330, 3350, 3360, 3362, 3370, 3380, 3388, 3390, 3410

Offset: 1

Author

Bernard Schott, Aug 03 2021

Keywords

• nonn
• base

Comments

The terminal digits are 00 or 44.

Examples

			150 is a term because 150^2 = 22500.
212 is a term because 212^2 = 44944 (smallest square with 2 times two 4's).
2788 is not a term because 2788^2 = 7772944.
		

Crossrefs

Subsequence of A346678.

Cf. A123912, A186438, A186439.

Programs

Mathematica

Select[Range[32, 3500], (d = IntegerDigits[#^2])[[1]] == d[[2]] != d[[3]] && d[[-1]] == d[[-2]] != d[[-3]] &] (* Amiram Eldar, Aug 03 2021 *)

Python

def ok(n):
    s = str(n*n)
    if len(s) < 4: return False # there are no ok squares with < 4 digits
    return s[0] == s[1] != s[2] and s[-1] == s[-2] != s[-3]
print(list(filter(ok, range(3411)))) # Michael S. Branicky, Aug 03 2021