A308527 Numbers that, for some x, are the concatenation of x+2, x+1 and x and are divisible by at least two of x+2, x+1 and x.

321, 432, 121110, 171615, 343332, 118117116, 232231230, 334333332, 333433333332, 452245214520, 333343333333332, 333334333333333332, 333333433333333333332, 333333343333333333333332

Offset

1,1

Comments

For each d>=1, (10^(3*d)-4)/3+10^(2*d) (the concatenation of x+2, x+1 and x where x = (10^d-4)/3) is in the sequence, being divisible by x+1 and x+3. Thus the sequence is infinite.

It appears that a(n) is of the form (10^(3*d)-4)/3+10^(2*d) for n >= 11. - Chai Wah Wu, Jun 19 2019

Links

Chai Wah Wu, Table of n, a(n) for n = 1..56

Example

232231230 is the concatenation of 232, 231 and 230, and is divisible by 231 and 230, so it is in the sequence.

Maple

f:=  proc(x)
  local t1, t2, q, a, b;
  t1:= 10^length(x);
  t2:= t1*10^length(x+1);
  q:= x*(1+t1+t2)+2*t2+t1;
    a:= (q/x)::integer;
  b:= (q/(x+1))::integer;
  if a and b then return q elif not(a) and not(b) then return NULL fi;
  if (q/(x+2))::integer then q else NULL fi
end proc:
map(f, [$1..10^8]);

Crossrefs

Cf. A306643.

Subsequence of A127424.

Sequence in context: A300849 A351994 A261262 * A268517 A228226 A004927

Adjacent sequences: A308524 A308525 A308526 * A308528 A308529 A308530

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Jun 05 2019

Status

approved