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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.
3
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.
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
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, May 23 2014
STATUS
approved