cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

Original entry on oeis.org

321, 432, 121110, 171615, 343332, 118117116, 232231230, 334333332, 333433333332, 452245214520, 333343333333332, 333334333333333332, 333333433333333333332, 333333343333333333333332
Offset: 1

Views

Author

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

Keywords

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

Examples

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

Crossrefs

Cf. A306643.
Subsequence of A127424.

Programs

  • 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]);