There are at least 2 identical digits in the result of a(n) * a(n+1). This is the lexicographically earliest sequence of distinct positive terms with this property (I hope). S = 1,11,2,22,3,33,10,20,5,23,7,16,9,13,17,15,35,19,6,24,12,21,25,4,28,8,... Examples 1 * 11 = 11 11 * 2 = 22 2 * 22 = 44 22 * 3 = 66 3 * 33 = 99 33 * 10 = 330 10 * 20 = 200 20 * 5 = 100 5 * 23 = 115 7 * 16 = 112 Etc. ____________________ Around midnight update > Giorgos Kalogeropoulos was quick to compute S ; here are the first 100 terms: S = 1, 11, 2, 22, 3, 33, 10, 20, 5, 23, 7, 16, 9, 13, 17, 15, 35, 19, 6, 24, 12, 21, 25, 4, 28, 8, 14, 18, 29, 31, 32, 34, 26, 38, 30, 36, 37, 27, 40, 45, 39, 41, 42, 44, 46, 47, 43, 52, 50, 48, 49, 51, 59, 56, 55, 57, 58, 54, 53, 61, 60, 65, 62, 67, 63, 68, 66, 64, 69, 71, 72, 70, 73, 75, 74, 78, 77, 76, 79, 81, 82, 80, 83, 85, 89, 84, 86, 90, 92, 87, 88, 91, 94, 97, 100, 93, 95, 101, 96, 102, ... > I didn't send a plot because it soon becomes a straig