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A338844 No prime digits are present in a(n) * a(n+1).

%I A338844 #18 Nov 20 2020 21:58:27
%S A338844 0,1,4,2,3,6,8,5,12,7,13,32,14,10,9,11,18,23,20,22,19,26,16,25,24,17,
%T A338844 38,28,30,27,33,36,29,21,39,49,34,35,40,15,44,41,46,88,50,80,51,91,54,
%U A338844 37,53,77,52,79,59,71,58,70,63,78,57,72,62,97,67,73,56,74,60,31,48,85,76,55,112,43,42,45
%N A338844 No prime digits are present in a(n) * a(n+1).
%C A338844 The prime digits are 2, 3, 5 and 7. This is the lexicographically earliest sequence of distinct nonnegative terms with this property and also a permutation of the nonnegative integers.
%H A338844 Carole Dubois, <a href="/A338844/b338844.txt">Table of n, a(n) for n = 1..5000</a>
%H A338844 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%e A338844 a(1) * a(2) = 0 * 1 = 0 (no prime digit is present);
%e A338844 a(2) * a(3) = 1 * 4 = 4 (no prime digit is present);
%e A338844 a(3) * a(4) = 4 * 2 = 8 (no prime digit is present);
%e A338844 a(4) * a(5) = 2 * 3 = 6 (no prime digit is present);
%e A338844 a(5) * a(6) = 3 * 6 = 18 (no prime digit is present); etc.
%t A338844 Block[{a = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], PrimeQ]], k++]; AppendTo[a, k]], {i, 2, 78}]; a] (* _Michael De Vlieger_, Nov 12 2020 *)
%Y A338844 Cf. A202268 (no prime digits).
%Y A338844 Cf. A338839, A338840, A338841, A338842, A338843, A338845, A338846 (variants on the same idea).
%K A338844 nonn,look,base
%O A338844 1,3
%A A338844 _Eric Angelini_ and _Carole Dubois_, Nov 11 2020