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A338839 No odd digit is present in a(n) + a(n+1).

%I A338839 #14 Nov 19 2020 23:56:01
%S A338839 0,2,4,16,6,14,8,12,10,18,22,20,24,36,26,34,28,32,30,38,42,40,44,156,
%T A338839 46,154,48,152,50,150,52,148,54,146,56,144,58,142,60,140,62,138,64,
%U A338839 136,66,134,68,132,70,130,72,128,74,126,76,124,78,122,80,120,82,118,84,116,86,114,88,112,90,110,92
%N A338839 No odd digit is present in a(n) + a(n+1).
%C A338839 This is the lexicographically earliest sequence of distinct nonnegative terms with this property.
%H A338839 Carole Dubois, <a href="/A338839/b338839.txt">Table of n, a(n) for n = 1..9999</a>
%e A338839 a(1) + a(2) = 0 + 2 = 2 (no odd digit is present);
%e A338839 a(2) + a(3) = 2 + 4 = 6 (no odd digit is present);
%e A338839 a(3) + a(4) = 4 + 16 = 20 (no odd digit is present); etc.
%t A338839 Block[{a = {0}}, Do[Block[{k = 2}, While[Nand[FreeQ[a, k], AllTrue[IntegerDigits@ Total[a[[-1]] + k], EvenQ]], k += 2]; AppendTo[a, k]], {i, 2, 71}]; a] (* _Michael De Vlieger_, Nov 12 2020 *)
%Y A338839 Cf. A014263 (no odd digit).
%Y A338839 Cf. A338840, A338841, A338842, A338843, A338844, A338845, A338846 (variants on the same idea).
%K A338839 base,nonn
%O A338839 1,2
%A A338839 _Eric Angelini_ and _Carole Dubois_, Nov 11 2020