A060812 Numbers whose square has a majority of one digit and does not end in 0.

1, 2, 3, 11, 12, 15, 21, 22, 26, 38, 109, 119, 131, 149, 165, 168, 173, 212, 216, 235, 258, 264, 298, 313, 738, 745, 1001, 1002, 1003, 1022, 1054, 1056, 1059, 1156, 1202, 1291, 1346, 1378, 1414, 1415, 1454, 1484, 1485, 1515, 1585, 1609, 1633, 1665, 1668

Offset

1,2

Comments

If 10^d < k < 10^d + 10^floor((2*d-3)/6), then k^2 has a majority of digits 0. In particular, the sequence is infinite. Robert Israel, Dec 20 2023

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

2038^2 = 4153444 and more than half the digits are 4's.

Maple

filter:= proc(n) local s, t, d;
  if n mod 10 = 0 then return false fi;
  s:= sort(convert(n^2, base, 10));
  d:= nops(s);
  t:= s[ceil(d/2)];
  numboccur(t, s) > d/2;
end proc:
select(filter, [$1..2000]); # Robert Israel, Dec 20 2023

Crossrefs

Sequence in context: A189818 A116032 A116029 * A212129 A172409 A062936

Adjacent sequences: A060809 A060810 A060811 * A060813 A060814 A060815

Keyword

base,easy,nonn

Author

Erich Friedman, Apr 29 2001

Status

approved