The Lucas Sequence has no Sequence Number, BUT ...

10/19/2015

The Lucas Sequence is defined as: a(1) = 2, a(2) = 1, and when n>2 then a(n) = a(n-1) + a(n-2) I was unable to find a Sequence Number for the Lucas Sequence.  But the following fraction does produce the terms of the Lucas Sequence, using three digit strings. 1999/998999 = 0. 002  001  003  004  007  011  018  029  047  076  123  199  322  521  … The fraction 1999999/999998999999 produces terms written in six digit strings.  And 1999999999999/999999999998999999999999 produces terms written in twelve digit strings. 1999999999999/999999999998999999999999 = 0. 000000000002..000000000001  000000000003  000000000004  000000000007  000000000011  000000000018  000000000029  000000000047  000000000076  000000000123  000000000199  000000000322  000000000521  000000000843  000000001364  000000002207  000000003571  000000005778  000000009349  000000015127  000000024476  000000039603  000000064079  000000103682  000000167761  000000271443  000000439204  000000710647  000001149851  000001860498  000003010349  000004870847  000007881196  000012752043  000020633239  000033385282  000054018521  000087403803  000141422324  000228826127  000370248451  000599074578  000969323029  001568397607  002537720636  004106118243  006643838879  010749957122  017393796001  028143753123  045537549124  073681302247  119218851371  192900153618  312119004989  505019158607  … Terms are written in 12 digit terms. Terms are accurate up to the 57th non-zero term. Compare with OEIS sequence A000032.

David