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%I #25 Nov 26 2019 08:34:36
%S 1,2,4,8,16,6,12,10,3,9,18,24,20,14,28,32,30,15,5,25,40,36,42,44,48,
%T 56,60,54,80,64,72,70,7,21,22,26,66,78,112,34,84,88,96,90,27,98,144,
%U 52,50,35,45,100,11,13,33,39,63,102,38,120,46,108,104,68,168
%N a(1)=1; a(n) is the smallest integer not yet in the sequence divisible by all nonzero digits of a(n-1).
%C A permutation of the naturals with inverse A237860.
%C If a(n) is a prime greater than 7 then no digit of a(n-1) is greater than 1, cf. A007088.
%H Lars Blomberg and Reinhard Zumkeller, <a href="/A237851/b237851.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t a[1] = 1;
%t a[n_] := a[n] = For[k = 1, True, k++, If[FreeQ[Array[a, n-1], k], If[ AllTrue[Select[IntegerDigits[a[n-1]], #>0&] // Union, Divisible[k, #]&], Return[k]]]];
%t a /@ Range[100] (* _Jean-François Alcover_, Nov 26 2019 *)
%o (Haskell)
%o import Data.List (nub, sort, delete)
%o a237851 n = a237851_list !! (n-1)
%o a237851_list = 1 : f 1 [2..] where
%o f x zs = g zs where
%o g (u:us) | all ((== 0) . (mod u)) ds = u : f u (delete u zs)
%o | otherwise = g us
%o where ds = dropWhile (<= 1) $
%o sort $ nub $ map (read . return) $ show x
%o -- _Reinhard Zumkeller_, Feb 14 2014
%Y Cf. A002796, A180410, A002473, A237860, A007088.
%K nonn,base,nice,look
%O 1,2
%A _Eric Angelini_, Feb 14 2014
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