A116287 Numbers k such that k*(k+3) gives the concatenation of a number m with itself.

8, 98, 767, 858, 910, 998, 3285, 6713, 9998, 45452, 54546, 99998, 990100, 999998, 8181819, 9999998, 70588233, 99999998, 343130554, 362637363, 363636361, 420053631, 421052632, 497975709, 502024289, 578947366, 579946367, 636363637, 637362635, 656869444, 706766918, 713286714, 714285712, 783689995

Offset

1,1

Comments

From Robert Israel, Apr 08 2025: (Start)

Numbers k such that k * (k + 3) = (10^d + 1) * m for some d and m where m has d digits.

Contains 10^d-2 for all d >= 1. (End)

Links

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

Maple

q:= proc(d, m) local R, t, a, b, x, q;
   t:= 10^d+1;
   R:= NULL;
   for a in numtheory:-divisors(t) do
     b:= t/a;
     if igcd(a, b) > 1 then next fi;
     for x from chrem([0, -m], [a, b]) by t do
       q:= x*(x+m)/t;
       if q >= 10^d then break fi;
       if q >= 10^(d-1) then R:= R, x fi;
   od od;
   sort(convert({R}, list));
end proc:
seq(op(q(d, 3)), d=1..10); # Robert Israel, Apr 08 2025

Crossrefs

Cf. A116130, A116280, A116286, A116288, A116296.

Sequence in context: A302527 A303409 A264168 * A290242 A116229 A099150

Adjacent sequences: A116284 A116285 A116286 * A116288 A116289 A116290

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

More terms from Robert Israel, Apr 08 2025

Status

approved