A346812 Positive numbers whose square starts with exactly 2 identical digits.

15, 21, 34, 47, 58, 67, 88, 94, 105, 106, 107, 108, 109, 150, 151, 182, 183, 184, 210, 211, 212, 235, 236, 257, 258, 278, 279, 297, 315, 316, 332, 333, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 470, 471, 473, 474, 475, 476, 477, 478, 479, 575, 576, 577, 578, 579, 580, 581

Offset: 1

Author

Bernard Schott, Aug 05 2021

Keywords

• nonn
• base

Comments

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

Examples

			34 is a term because 34^2 = 1156.
149 is not a term because 149^2 = 22201.
		

Crossrefs

Subsequence of A123912.

A346774 is a subsequence.

Cf. A186438, A186439, A346678 (similar, with "ends").

Programs

Mathematica

Select[Range[10, 600], (d = IntegerDigits[#^2])[[1]] == d[[2]] != d[[3]] &] (* Amiram Eldar, Aug 05 2021 *)

PARI

isok(m) = my(d=digits(m^2)); (#d > 2) && (d[2] == d[1]) && (d[3] != d[2]); \\ Michel Marcus, Aug 05 2021

Python

def ok(n): s = str(n*n); return len(s) > 2 and s[0] == s[1] != s[2]
print(list(filter(ok, range(582)))) # Michael S. Branicky, Aug 05 2021