

A331026


Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the nth nonzero decimal digit in the sequence divides the nth 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
(list;
graph;
refs;
listen;
history;
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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 nth has A055640(a(n)) terms, and T(n, k) is a multiple of the kth nonzero digit of a(n).


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A331026
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

For first terms and corresponding digits are:
n a(n) nth 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: A297289 A048327 A048340 * A098312 A279487 A046039
Adjacent sequences: A331023 A331024 A331025 * A331027 A331028 A331029


KEYWORD

nonn,base,look,tabf


AUTHOR

Rémy Sigrist, Jan 07 2020


STATUS

approved



