This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338843 #21 Nov 20 2020 21:59:15
%S A338843 0,1,3,5,4,2,6,8,10,9,7,11,29,12,28,13,27,14,26,15,25,16,24,17,23,18,
%T A338843 22,19,21,20,40,41,39,30,31,33,35,34,32,36,44,37,43,38,42,46,45,49,47,
%U A338843 51,48,50,54,52,56,53,55,59,57,61,58,60,80,64,76,65,75,66,74,67,73,68,72,69,71,70,78,62
%N A338843 No prime digit is present in a(n) + a(n+1).
%C A338843 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 A338843 Carole Dubois, <a href="/A338843/b338843.txt">Table of n, a(n) for n = 1..5000</a>
%H A338843 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%e A338843 a(1) + a(2) = 0 + 1 = 1 (no prime digit is present);
%e A338843 a(2) + a(3) = 1 + 3 = 4 (no prime digit is present);
%e A338843 a(3) + a(4) = 3 + 5 = 8 (no prime digit is present); etc.
%t A338843 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 A338843 Cf. A202268 (no prime digits).
%Y A338843 Cf. A338839, A338840, A338841, A338842, A338844, A338845, A338846 (variants on the same idea).
%K A338843 nonn,look,base
%O A338843 1,3
%A A338843 _Eric Angelini_ and _Carole Dubois_, Nov 11 2020