A242810 a(n) is the smallest n-digit number whose truncation after its first k digits is divisible by the k-th Lucas number (A000032(n)) for k = 1..n.

1, 12, 120, 1204, 12045, 120456, 3689467, 36894671, 368946712

Offset

1,2

Comments

There are 9 terms in the series and 9-digit number 368946712

is the last number to satisfy the requirements.

Links

Table of n, a(n) for n=1..9.

Example

  368946712 is divisible by Lucas(9) = 76;
   36894671 is divisible by Lucas(8) = 47;
    3689467 is divisible by Lucas(7) = 29;
     368946 is divisible by Lucas(6) = 18;
      36894 is divisible by Lucas(5) = 11;
       3689 is divisible by Lucas(4) =  7;
        368 is divisible by Lucas(3) =  4;
         36 is divisible by Lucas(2) =  3;
          3 is divisible by Lucas(1) =  1.

Mathematica

a=Table[j, {j, 1, 10, 2}]; r=2; t={}; While[!a == {}, n=Length[a]; nmin=First[a]; k=1; b={}; While[!k>n, z0=a[[k]]; Do[z=10*z0+j; If[Mod[z, LucasL[r]]==0, b=Append[b, z]], {j, 0, 9}]; k++]; AppendTo[t, nmin]; a=b; r++]; t

Crossrefs

Cf. A000032, A225614, A242808, A242809, A242811.

Sequence in context: A001754 A037511 A037694 * A067102 A361573 A129064

Adjacent sequences: A242807 A242808 A242809 * A242811 A242812 A242813

Keyword

nonn,base,fini,full

Author

Michel Lagneau, May 23 2014

Status

approved