Hello Math-Fun Today we'll look at the arithmetic mean of the digits used so far in a sequence S. S = 45, 30, 200, 204, 2006, 2015, 2024, 227, 258, 26, ... The arithmetic mean of the digits used by the 1st term is 4.5 [(4+5)/2 = 9/2 = 4.5] The arithmetic mean of the digits used by the first 2 terms is 3.0 [(4+5+3+0 )/4 = 12/4 = 3.0] The arithmetic mean of the digits used by the first 3 terms is 2.0 [(4+5+3+0+2+0+0)/7 = 14/7 = 2.0] The arithmetic mean of the digits used by the first 4 terms is also 2.0 [20/10 = 2.0] And so is the arithmetic mean of the digits used by the first 5 terms: 2.0 [28/14 = 2.0] By the first 6 terms: 2.0 [36/18 = 2.0] By the first 7 terms: 2.0 [44/22 = 2.0] By the first 8 terms: 2.2 [53/25 = 2.2] By the first 9 terms: 2.5 [70/28 = 2.5] By the first 10 terms: 2.6 [78/30 = 2.6] Etc. Many sequences have this property – but S is the lexicographically earliest of distinct terms with this property (I hope!) In other words: « The first two digits of a(n) form a number which is 10/n times the sum of the digits used so far by S ». Any taker to extend S? Best, É.