A242809 - OEIS

%I #10 Sep 17 2017 18:43:40

%S 9,99,998,9987,99875,998752,9987523,99840006,994552020,9945520200,

%T 95880078250

%N 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.

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

%e   95880078250 is divisible by Fibonacci(11) = 89;

%e    9588007825 is divisible by Fibonacci(10) = 55;

%e     958800782 is divisible by Fibonacci(9)  = 34;

%e      95880078 is divisible by Fibonacci(8)  = 21;

%e       9588007 is divisible by Fibonacci(7)  = 13;

%e        958800 is divisible by Fibonacci(6)  =  8;

%e         95880 is divisible by Fibonacci(5)  =  5;

%e          9588 is divisible by Fibonacci(4)  =  3;

%e           958 is divisible by Fibonacci(3)  =  2;

%e            95 is divisible by Fibonacci(2)  =  1;

%e             9 is divisible by Fibonacci(1)  =  1.

%t 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

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

%K nonn,base,fini,full

%O 1,1

%A _Michel Lagneau_, May 23 2014