A116290 Numbers k such that k * (k+6) is the concatenation of a number m with itself.

5, 95, 462, 533, 715, 819, 995, 3425, 6570, 9995, 90904, 99995, 980199, 999995, 3636358, 6363637, 9999995, 41176465, 58823530, 99999995, 413533835, 426573427, 428571423, 432620006, 567379989, 571428572, 573426568, 586466160, 686261108, 725274726, 727272722

Offset

1,1

Comments

From Robert Israel, Apr 08 2025: (Start)

Numbers k such that k * (k + 6) = (10^d + 1) * m for some d and m where m has d digits.

Contains 10^d-5 for all d >= 1. (End)

Links

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

Maple

f:= proc(d) 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, -6], [a, b]) by t do
       q:= x*(x+6)/t;
       if q >= 10^d then break fi;
       if q >= 10^(d-1) then R:= R, x fi;
   od od;
   sort([R]);
end proc:
seq(op(f(d)), d=1..10); # Robert Israel, Apr 08 2025

Crossrefs

Cf. A116159, A116282, A116289, A116291, A116304.

Sequence in context: A153227 A116159 A054205 * A274874 A275292 A383648

Adjacent sequences: A116287 A116288 A116289 * A116291 A116292 A116293

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

Name edited by Robert Israel, Apr 08 2025

Status

approved