A375211 Complement of A129459.

3, 4, 5, 7, 9, 16, 18, 19, 23, 25, 33, 34, 38, 43, 45, 48, 49, 54, 56, 58, 59, 66, 77, 79, 84, 86, 93, 144, 149, 155, 157, 166, 176, 189, 195, 223, 233, 238, 243, 258, 266, 293, 295, 304, 308, 313, 314, 323, 333, 334, 344, 376, 378, 388, 393, 404, 423, 433, 435, 443, 448, 457, 459, 566, 576, 579

Offset

1,1

Comments

Given positive integer x, let y be the greatest integer < x that is not in the sequence (and thus is a member of A129459). Then x is in the sequence iff neither x nor y share any decimal digit with x * y.

For each k >= 1, at least one of (10^k - 1)/3 = 3...33 and (10^k + 2)/3 = 3...34 is in the sequence, as their product is (10^(2*k) + 10^k - 2)/9 = 1..12...2. Similarly, at least one of (2*10^k - 2)/3 = 6...66 and (2*10^k + 1)/3 = 6...67 is in the sequence. In particular, the sequence is infinite.

Links

Robert Israel, Table of n, a(n) for n = 1..5000

Example

a(6) = 16 is a term because 15 is the greatest integer < 16 that is not in the sequence, and neither 16 nor 15 shares a digit with 16 * 15 = 240.

Maple

f:= proc(n) local Ln, Lk, k;
  Ln:= convert(convert(n, base, 10), set);
  for k from n+1 do
     Lk:= convert(convert(k, base, 10), set) union Ln;
     if convert(convert(n*k, base, 10), set) intersect Lk <> {} then return k fi
  od
end proc:
R:= NULL: x:= 0: count:= 0:
while count < 100 do
  y:= f(x);
  count:= count + y - x - 1;
  R:= R, $(x+1)..(y-1);
  x:= y
od:
R;

Crossrefs

Cf. A129459.

Sequence in context: A036971 A000702 A067526 * A101760 A165713 A105148

Adjacent sequences: A375208 A375209 A375210 * A375212 A375213 A375214

Keyword

nonn,base,look

Author

Robert Israel, Feb 06 2025

Status

approved