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

1,1

Comments

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

Links

Table of n, a(n) for n=1..60.

Example

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A123912.

A346774 is a subsequence.

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

Sequence in context: A190358 A090999 A123912 * A296244 A309005 A225916

Adjacent sequences: A346809 A346810 A346811 * A346813 A346814 A346815

Keyword

nonn,base

Author

Bernard Schott, Aug 05 2021

Status

approved