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a(n) = 1, a(n+1) = smallest number not occurring earlier, having with a(n) neither a common digit nor a common divisor.
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%I #8 Sep 17 2016 12:38:46

%S 1,2,3,4,5,6,7,8,9,10,23,11,20,13,22,15,26,17,24,19,25,14,27,16,29,18,

%T 35,12,37,21,34,55,28,31,40,33,41,30,47,32,45,38,49,36,59,42,53,44,39,

%U 46,51,43,50,61,48,65,71,52,63,58,67,54,73,56,79,60,77

%N a(n) = 1, a(n+1) = smallest number not occurring earlier, having with a(n) neither a common digit nor a common divisor.

%H Reinhard Zumkeller, <a href="/A239664/b239664.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o import Data.List (delete, intersect); import Data.Function (on)

%o a239664 n = a239664_list !! (n-1)

%o a239664_list = 1 : f 1 [2..] where

%o f v ws = g ws where

%o g (x:xs) = if gcd v x == 1 && ((intersect `on` show) v x == "")

%o then x : f x (delete x ws) else g xs

%o (PARI) {u=[]; a=1; for(n=1,99, print1(a","); u=setunion(u,[a]); while(#u>1&&u[2]==u[1]+1,u=u[^1]); for(k=u[1]+1,9e9, setsearch(u,k)&&next;gcd(k,a)>1&&next; #setintersect(Set(digits(a)),Set(digits(k)))&&next; a=k; next(2)));a} \\ _M. F. Hasler_, Sep 17 2016

%Y Cf. A054659, A067581, A276633, A276512.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Mar 23 2014