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A346774
Numbers whose square starts and ends with exactly 2 identical digits.
6
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
1,1
COMMENTS
The terminal digits are 00 or 44.
EXAMPLE
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.
MATHEMATICA
Select[Range[32, 3500], (d = IntegerDigits[#^2])[[1]] == d[[2]] != d[[3]] && d[[-1]] == d[[-2]] != d[[-3]] &] (* Amiram Eldar, Aug 03 2021 *)
PROG
(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
CROSSREFS
Subsequence of A346678.
Sequence in context: A039445 A300144 A247528 * A249555 A226587 A044258
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Aug 03 2021
STATUS
approved