A242809 a(n) is the largest n-digit number whose truncation after its first k digits is divisible by the k-th Fibonacci number for k = 1..n.

9, 99, 998, 9987, 99875, 998752, 9987523, 99840006, 994552020, 9945520200, 95880078250

Offset

1,1

Comments

There are 11 terms in the series and 11-digit number 95880078250 is the last number to satisfy the requirements.

Links

Table of n, a(n) for n=1..11.

Example

  95880078250 is divisible by Fibonacci(11) = 89;
   9588007825 is divisible by Fibonacci(10) = 55;
    958800782 is divisible by Fibonacci(9)  = 34;
     95880078 is divisible by Fibonacci(8)  = 21;
      9588007 is divisible by Fibonacci(7)  = 13;
       958800 is divisible by Fibonacci(6)  =  8;
        95880 is divisible by Fibonacci(5)  =  5;
         9588 is divisible by Fibonacci(4)  =  3;
          958 is divisible by Fibonacci(3)  =  2;
           95 is divisible by Fibonacci(2)  =  1;
            9 is divisible by Fibonacci(1)  =  1.

Mathematica

a=Table[j, {j, 3, 10, 2}]; r=2; t={}; While[!a == {}, n=Length[a]; nmax=Last[a]; k=1; b={}; While[!k>n, z0=a[[k]]; Do[z=10*z0+j; If[Mod[z, Fibonacci[r]]==0, b=Append[b, z]], {j, 0, 9}]; k++]; AppendTo[t, nmax]; a=b; r++]; t

Crossrefs

Cf. A000045, A225614, A242808, A242810, A242811.

Sequence in context: A242811 A070843 A261512 * A108908 A116260 A103456

Adjacent sequences: A242806 A242807 A242808 * A242810 A242811 A242812

Keyword

nonn,base,fini,full

Author

Michel Lagneau, May 23 2014

Status

approved