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%I #13 Jan 09 2020 19:22:31
%S 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 28,26,35,27,36,32,40,34,29,33,38,42,44,39,46,48,50,54,45,55,52,49,51,
%U 60,57,56,64,63,68,58,72,66,69,75,80,76,62,84,88,78,81
%N 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 This sequence is a permutation of the natural numbers:
%C - necessarily some nonzero digit, say d, appears infinitely many times,
%C - if d=1, then we have infinitely many multiples of 1, and eventually every number will show up,
%C - 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 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 Rémy Sigrist, <a href="/A331026/b331026.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A331026/a331026.gp.txt">PARI program for A331026</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e For first terms and corresponding digits are:
%e n a(n) n-th digit
%e -- ---- ----------
%e 1 1 1
%e 2 2 2
%e 3 3 3
%e 4 4 4
%e 5 5 5
%e 6 6 6
%e 7 7 7
%e 8 8 8
%e 9 9 9
%e 10 10 1
%e 11 11 1
%e 12 12 1
%e 13 13 1
%e 14 14 2
%o (PARI) See Links section.
%Y See A331010 for similar sequences.
%Y Cf. A055640.
%K nonn,base,look,tabf
%O 1,2
%A _Rémy Sigrist_, Jan 07 2020
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