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.

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

Author

Rémy Sigrist, Jan 07 2020

Keywords

• nonn
• base
• look
• tabf

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).

Examples

			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
		

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

Crossrefs

See A331010 for similar sequences.

Cf. A055640.

Programs

PARI

\\ See Links section.