OFFSET
1,2
COMMENTS
"Lexicographically earliest injective sequence" means that a(n+1) is the least positive integer not occurring earlier with the given property.
Conjectured to be a permutation of the positive integers, which is the case if and only if an infinite number of terms have a digit "1".
Conjecture: For nonnegative integer x, 2*10^x appears at index 2*10^x (see A226179). Hans Havermann, May 29 2013
Fixed points, i.e., indices n for which a(n)=n, are listed in A226179. - M. F. Hasler, May 30 2013
B. Jubin and H. Havermann made remarks about this sequence in other bases, its fractal nature and fixed points: See the link to the SeqFan list. - M. F. Hasler, May 30 2013
LINKS
Paul Tek, Table of n, a(n) for n = 1..10000
B. Jubin and others, in reply to E. Angelini's post a(n+1) is the multiple of at least one digit of a(n), SeqFan list, May 29 2013.
PROG
(PARI) A218468(n, a=[1])={ for(n=1, n-1, print1(a[#a]", "); my(d=digits(a[#a])); for(k=2, 9e9, setsearch(Set(a), k) || for(i=1, #d, !d[i] || k%d[i] || !(a=concat(a, k)) || next(3)))); a[#a]} \\ could be optimized...
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and M. F. Hasler, May 28 2013
STATUS
approved