A218468 a(n+1) is a multiple of at least one digit of a(n); this is the lexicographically earliest injective such sequence.

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

Author

Eric Angelini and M. F. Hasler, May 28 2013

Keywords

• nonn
• base

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.

Programs

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...