login
A331026
Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the n-th nonzero decimal digit in the sequence divides the n-th term.
2
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 16, 20, 17, 25, 19, 24, 21, 30, 22, 23, 28, 26, 35, 27, 36, 32, 40, 34, 29, 33, 38, 42, 44, 39, 46, 48, 50, 54, 45, 55, 52, 49, 51, 60, 57, 56, 64, 63, 68, 58, 72, 66, 69, 75, 80, 76, 62, 84, 88, 78, 81
OFFSET
1,2
COMMENTS
This sequence is a permutation of the natural numbers:
- necessarily some nonzero digit, say d, appears infinitely many times,
- if d=1, then we have infinitely many multiples of 1, and eventually every number will show up,
- if d>1, then all the multiples of d will show up, as there are infinitely many multiples of d containing a "1" digit, we have infinitely many multiples of 1 as well, and eventually every number will show up.
This sequence can also be seen as an irregular table, where the n-th has A055640(a(n)) terms, and T(n, k) is a multiple of the k-th nonzero digit of a(n).
EXAMPLE
For first terms and corresponding digits are:
n a(n) n-th digit
-- ---- ----------
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
10 10 1
11 11 1
12 12 1
13 13 1
14 14 2
PROG
(PARI) See Links section.
CROSSREFS
See A331010 for similar sequences.
Cf. A055640.
Sequence in context: A048327 A048340 A372658 * A098312 A279487 A046039
KEYWORD
nonn,base,look,tabf
AUTHOR
Rémy Sigrist, Jan 07 2020
STATUS
approved