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A218468
a(n+1) is a multiple of at least one digit of a(n); this is the lexicographically earliest injective such sequence.
3
1, 2, 4, 8, 16, 3, 6, 12, 5, 10, 7, 14, 9, 18, 11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 30, 21, 23, 27, 32, 33, 36, 39, 42, 34, 40, 44, 48, 52, 25, 35, 45, 50, 55, 60, 54, 56, 65, 66, 72, 38, 51, 29, 46, 64, 68, 78, 49, 63, 57, 70, 77, 84, 76, 90, 81, 31, 37, 69, 96, 99, 108, 41, 43, 75, 80, 88, 104, 47, 91, 53, 85, 95, 100, 58, 105, 59, 110, 61, 62
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
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
Sequence in context: A339853 A373944 A218338 * A308539 A036122 A050124
KEYWORD
nonn,base
AUTHOR
Eric Angelini and M. F. Hasler, May 28 2013
STATUS
approved