A088287 Palindromes divisible by the number formed by their internal digits.

111, 212, 222, 313, 333, 414, 424, 444, 515, 555, 616, 626, 636, 666, 717, 777, 818, 828, 848, 888, 919, 939, 999, 1111, 1771, 2112, 2222, 2772, 3113, 3333, 3773, 4114, 4224, 4444, 4774, 5115, 5555, 5775, 6116, 6226, 6336, 6666, 6776, 7117, 7777, 8118, 8228, 8448, 8778, 8888, 9119, 9339, 9779, 9999, 42924, 79597, 82928

Offset

1,1

Comments

a(58) > 10^1000 if it exists. - Robert Israel, Jan 14 2025

Links

Table of n, a(n) for n=1..57.

Example

2772 is a member as it is divisible by 77.

Maple

goodpali:= proc(n, d) local L; L:= convert(n, base, 10); nops(L)=d and L = ListTools:-Reverse(L) end proc:
f:= proc(d) # terms with d digits
  local ex, j, S, W;
  S:= {};
  for j from 1 to 9 do
    ex:= j * (10^(d-1)+1);
    W:= select(w -> ex mod w = 0, {$ ceil(ex/10^(d-2)) .. floor(ex/10^(d-3))});
    S:= S union map(t -> 10*t + ex, select(goodpali, map(w -> ex/w, W), d-2));
  od;
op(convert(S, list))
end proc:
seq(f(d), d=3..5); # Robert Israel, Jan 14 2025

Crossrefs

Sequence in context: A172189 A279777 A291797 * A082946 A392225 A082945

Adjacent sequences: A088284 A088285 A088286 * A088288 A088289 A088290

Keyword

base,nonn

Author

Amarnath Murthy, Sep 29 2003

Extensions

More terms from David Wasserman, Aug 04 2005

a(47)-a(57) from Robert Israel, Jan 14 2025

Status

approved