%I
%S 1,2,4,5,6,3,9,12,15,8,7,11,10,14,13,17,16,20,19,23,22,24,18,21,27,30,
%T 33,36,39,42,25,26,28,29,31,32,34,35,37,38,40,41,43,44,45,46,47,49,48,
%U 50,52,53,54,51,55,56,58,59,60,57,63,66,62,61,64,65,67,68,70,71,73,74,76,77,79,80,82,83,84,69,72,75,78
%N Take all the digits of a(n) and a(n+1) then reorder them in a single integer: this will never produce a prime, no matter the rearrangement.
%C The sequence is always extended with the smallest integer not yet present that doesn't lead to a contradiction.
%C The sequence is infinite and might be a permutation of the integers > 0.
%H JeanMarc Falcoz, <a href="/A287224/b287224.txt">Table of n, a(n) for n = 1..1301</a>
%e The first two terms are 1 and 2 because neither 12 or 21 are primes; the next term cannot be 3 as 23 is prime; 4 is ok because neither 24 nor 42 are primes; the next term cannot be 3 as 43 is prime; etc.
%t a = {{1}}; Do[k = 1; While[Nand[! MemberQ[a, #], NoneTrue[Map[FromDigits, Permutations[a[[n  1]]~Join~#]], PrimeQ]] &@ Set[d, IntegerDigits@ k], k++]; AppendTo[a, d], {n, 2, 83}]; FromDigits /@ a (* _Michael De Vlieger_, May 22 2017 *)
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _JeanMarc Falcoz_, May 22 2017
