A242808 The smallest n-digit number where first k digits are divisible by k-th Fibonacci number for k = 1..n.

1, 10, 100, 1002, 10020, 100200, 1002001, 10050432, 100552416, 1023529540, 15035286200

Offset

1,2

Comments

There are 11 terms in the series and 11-digit number 15035286200 is the last number to satisfy the requirements.

Links

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

Example

15035286200 is divisible by fibonacci(11)= 89
1503528620 is divisible by fibonacci(10)= 55
150352862 is divisible by fibonacci(9)= 34
15035286 is divisible by fibonacci(8)= 21
1503528 is divisible by fibonacci(7)= 13
150352 is divisible by fibonacci(6)= 8
15035 is divisible by fibonacci(5)= 5
1503 is divisible by fibonacci(4)= 3
150 is divisible by fibonacci(3)= 2
15 is divisible by fibonacci(2)= 1
1 is divisible by fibonacci(1)= 1

Mathematica

a=Table[j, {j, 1, 15, 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, Fibonacci[r]]==0, b=Append[b, z]], {j, 0, 9}]; k++]; AppendTo[t, nmin]; a=b; r++]; t

Crossrefs

Cf. A000045, A225614, A242809, A242810, A242811.

Sequence in context: A267156 A267524 A259883 * A304453 A277916 A283088

Adjacent sequences: A242805 A242806 A242807 * A242809 A242810 A242811

Keyword

nonn,base,fini,full

Author

Michel Lagneau, May 23 2014

Status

approved