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A248024 Lexicographically earliest permutation of the positive integers such that the first digit of a(n+1) divides a(n).

%I A248024 #25 Dec 23 2024 14:53:44
%S A248024 1,10,2,11,12,3,13,14,7,15,5,16,4,17,18,6,19,100,20,21,30,22,23,101,
%T A248024 102,24,8,25,50,26,27,9,31,103,104,28,29,105,32,40,41,106,107,108,33,
%U A248024 34,109,110,51,35,52,42,36,37,111,38,112,43,113,114,39,115,53,116,44,45,54,60
%N A248024 Lexicographically earliest permutation of the positive integers such that the first digit of a(n+1) divides a(n).
%H A248024 Reinhard Zumkeller, <a href="/A248024/b248024.txt">Table of n, a(n) for n = 1..10000</a>
%H A248024 Eric Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-September/013710.html">Quick and fun permutation</a>, SeqFan list, Sep 29 2014
%H A248024 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t A248024 a[1] = 1; a[n_] := a[n] = Block[{k = 2}, While[Mod[a[n - 1], First@IntegerDigits[k]] != 0 || MemberQ[Array[a, n - 1], k], k++]; k]; Array[a, 68] (* _Giorgos Kalogeropoulos_, May 12 2023 *)
%o A248024 (PARI) a(n,S=1,u=2)=for(i=1,n,print1(S",");for(k=1,9e9,bittest(u,k)&&next;S%digits(k)[1]&&next;u+=1<<S=k;break));S
%o A248024 (Haskell)
%o A248024 import Data.List (delete)
%o A248024 a248024 n = a248024_list !! (n-1)
%o A248024 a248024_list = 1 : f 1 [2..] where
%o A248024   f x zs = g zs where
%o A248024     g (y:ys) = if x `mod` (a000030 y) == 0
%o A248024                then y : f y (delete y zs) else g ys
%o A248024 -- _Reinhard Zumkeller_, Sep 30 2014
%Y A248024 Cf. A248043 (inverse), A000030.
%K A248024 nonn,base,look
%O A248024 1,2
%A A248024 _Eric Angelini_ and _M. F. Hasler_, Sep 29 2014