1,1

A self-describing sequence. See the sequence as a succession of digits: then a(n) is the position of the even digits of the sequence.

"Lexicographically earliest" refers to comparing sequences term by term, not the strings obtained by the concatenation. (This is not possible, since then the 1st term could be an arbitrarily long string of 1's.) In other words, term after term, the smallest possible value not leading to a contradiction is appended.

We can't have a(1)=1 (since then the 1st digit would not be even) nor a(1)=2 (since then the 1st digit would be even), but a(1)=3 is possible.

This implies that there follows another odd digit, a(2)=5, before the first even digit a(a(1))=a(3)=6.

Then comes another odd digit, a(4)=7, since the second even digit occurs only in position a(2)=5, namely a(5)=8.

______________________ 1 _________________ 2 _________________ 3 _ ...

pos. 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 ...

seq. 3,5,6,7,8,2 0,2 1,3 1,3 3,3 5,3 7,3 9,4 0,5 1,5 3,5 5,5 7,5 8,...

The even digits of the sequence are between parentheses here:

Sequence: 3,5,(6),7,(8),(2)(0),(2)1,31,33,35,37,39,(4)(0)...

Positions of even digits: 3, 5, 6, 7, 8, 20, 21... = the sequence itself

base,easy,more,nonn,nice,new

Eric Angelini (eric.angelini(AT)kntv.be), Feb 05 2006

Edited by M. F. Hasler, Dec 06 2009

Further edits by njas, Dec 19 2009