A346678 Positive numbers whose squares end in exactly two identical digits.

10, 12, 20, 30, 40, 50, 60, 62, 70, 80, 88, 90, 110, 112, 120, 130, 138, 140, 150, 160, 162, 170, 180, 188, 190, 210, 212, 220, 230, 238, 240, 250, 260, 262, 270, 280, 288, 290, 310, 312, 320, 330, 338, 340, 350, 360, 362, 370, 380, 388, 390, 410, 412, 420, 430, 438, 440, 450, 460

Offset

1,1

Comments

When a square ends in exactly two identical digits, these digits are necessarily 00 or 44, so all terms are even.

The numbers are of the form: 10*floor((10*k-1)/9), k > 0, or, 50*floor((10*k-1)/9) +- 38, k > 0.

Equivalently: m is in the sequence iff either (m == 0 (mod 10) and m <> 0 (mod 100)) or (m == +- 38 (mod 50) and m <> +- 38 (mod 500)).

Links

Table of n, a(n) for n=1..59.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

a(n+63) = a(n) + 500.

Example

12 is in the sequence because 12^2 = 144 ends in two 4's.
20 is in the sequence because 20^2 = 400 ends in two 0's.
38 is not in the sequence because 38^2 = 1444 ends in three 4's.

Mathematica

Select[Range[10, 460], (d = IntegerDigits[#^2])[[-1]] == d[[-2]] != d[[-3]] &] (* Amiram Eldar, Jul 29 2021 *)

Prog

(Python)
def ok(n): s = str(n*n); return len(s) > 2 and s[-1] == s[-2] != s[-3]
print(list(filter(ok, range(461)))) # Michael S. Branicky, Jul 29 2021

Crossrefs

Equals A186438 \ A186439.

Supersequence of A346774.

Sequence in context: A085772 A162189 A186438 * A035284 A265403 A215940

Adjacent sequences: A346675 A346676 A346677 * A346679 A346680 A346681

Keyword

nonn,base,easy

Author

Bernard Schott, Jul 29 2021

Status

approved