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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.

%I A331026 #16 Apr 29 2025 19:13:31
%S A331026 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,
%T A331026 28,26,35,27,36,32,40,34,29,33,38,42,44,39,46,48,50,54,45,55,52,49,51,
%U A331026 60,57,56,64,63,68,58,72,66,69,75,80,76,62,84,88,78,81
%N 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.
%C A331026 This sequence is a permutation of the natural numbers:
%C A331026 - necessarily some nonzero digit, say d, appears infinitely many times,
%C A331026 - if d=1, then we have infinitely many multiples of 1, and eventually every number will show up,
%C A331026 - 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.
%C A331026 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).
%H A331026 Rémy Sigrist, <a href="/A331026/b331026.txt">Table of n, a(n) for n = 1..10000</a>
%H A331026 Rémy Sigrist, <a href="/A331026/a331026.gp.txt">PARI program for A331026</a>
%H A331026 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A331026 For first terms and corresponding digits are:
%e A331026   n   a(n)  n-th digit
%e A331026   --  ----  ----------
%e A331026    1     1           1
%e A331026    2     2           2
%e A331026    3     3           3
%e A331026    4     4           4
%e A331026    5     5           5
%e A331026    6     6           6
%e A331026    7     7           7
%e A331026    8     8           8
%e A331026    9     9           9
%e A331026   10    10           1
%e A331026   11    11           1
%e A331026   12    12           1
%e A331026   13    13           1
%e A331026   14    14           2
%o A331026 (PARI) \\ See Links section.
%Y A331026 See A331010 for similar sequences.
%Y A331026 Cf. A055640.
%K A331026 nonn,base,look,tabf
%O A331026 1,2
%A A331026 _Rémy Sigrist_, Jan 07 2020