A338841 - OEIS

%I #20 Nov 20 2020 21:57:04

%S 0,1,2,3,8,5,4,6,7,12,17,24,10,20,11,22,13,16,14,19,32,9,52,39,58,36,

%T 18,26,31,28,15,40,21,42,53,54,46,44,47,60,34,59,38,69,94,30,68,33,62,

%U 43,48,50,56,73,88,23,96,25,80,35,64,41,104,27,84,51,122,71,66,37,72,29,76,79,112,74,63,102,61

%N No odd digit is present in a(n) * a(n+1).

%C This is the lexicographically earliest sequence of distinct nonnegative terms with this property and also a permutation of the nonnegative integers.

%H Carole Dubois, <a href="/A338841/b338841.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>

%e a(1) * a(2) = 0 * 1 = 0 (no odd digit is present);

%e a(2) * a(3) = 1 * 2 = 2 (no odd digit is present);

%e a(3) * a(4) = 2 * 3 = 6 (no odd digit is present);

%e a(4) * a(5) = 3 * 8 = 24 (no odd digit is present); etc.

%t Block[{a = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], OddQ]], k++]; AppendTo[a, k]], {i, 2, 79}]; a] (* _Michael De Vlieger_, Nov 12 2020 *)

%Y Cf. A014263 (no odd digits).

%Y Cf. A338839, A338840, A338842, A338843, A338844, A338845, A338846 (variants on the same idea).

%K nonn,base,look

%O 1,3

%A _Eric Angelini_ and _Carole Dubois_, Nov 11 2020