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

1,1

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.

Links

Table of n, a(n) for n=1..41.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A346941, A346942.

Supersequences: A131573, A132391.

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

Sequence in context: A220626 A136420 A132391 * A134966 A108419 A073037

Adjacent sequences: A346937 A346938 A346939 * A346941 A346942 A346943

Keyword

nonn,base

Author

Bernard Schott, Aug 08 2021

Status

approved