A346940 Numbers whose square starts with exactly 4 identical digits.

2357, 2582, 3334, 4714, 5774, 6667, 8165, 8819, 9428, 10542, 10543, 10544, 10545, 14907, 14908, 14909, 18257, 18258, 18259, 21081, 21082, 21083, 23570, 23571, 25819, 25820, 27888, 27889, 29813, 29814, 31622, 33332, 33333, 33335, 33336, 33337, 33338, 33339, 33340, 33341, 33342

Offset: 1

Author

Bernard Schott, Aug 08 2021

Keywords

• nonn
• base

Comments

If m is a term, 10*m is another term.

Differs from A132391 where only at least 4 identical digits are required; indeed, 10541 is the first term of A132391 that is not in this sequence (see Example section), the next one is 33346.

Examples

			2357 is a term because 2357^2 = 5555449 starts with four 5's.
10541 is not a term because 10541^2 = 111112681 starts with five 1's.
		

Crossrefs

Cf. A346941, A346942.

Supersequences: A131573, A132391.

Similar with: A346812 (2 digits), A346891 (3 digits).

Programs

Mathematica

q[n_] := SameQ @@ (d = IntegerDigits[n^2])[[1 ;; 4]] && d[[5]] != d[[1]]; Select[Range[100, 33350], q] (* Amiram Eldar, Aug 08 2021 *)

Python

def ok(n):
    s = str(n*n)
    return len(s) > 4 and s[0] == s[1] == s[2] == s[3] != s[4]
print(list(filter(ok, range(33343)))) # Michael S. Branicky, Aug 08 2021