MathDB
2016 Guts #33

Source:

December 24, 2016

Problem Statement

<spanclass=′latex−bold′>(LucasNumbers)</span><span class='latex-bold'>(Lucas Numbers)</span> The Lucas numbers are defined by L0=2L_0 = 2, L1=1L_1 = 1, and Ln+2=Ln+1+LnL_{n+2} = L_{n+1} + L_n for every n≥0n \ge 0. There are NN integers 1≤n≤20161 \le n \le 2016 such that LnL_n contains the digit 11. Estimate NN.
An estimate of EE earns ⌊20−2∣N−E∣⌋\left\lfloor 20 - 2|N-E| \right\rfloor or 00 points, whichever is greater.
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