cp's OEIS Frontend

A335743 Keep the first two digits of a(n) and insert a dot between them; this is now the arithmetic mean (truncated after the first decimal) of the digits used so far in the sequence. Lexicographically earliest sequence of distinct positive terms with this property.

%I A335743 #17 Jul 03 2020 06:58:57
%S A335743 45,30,38,301,306,307,305,308,304,318,303,309,316,302,2900,2901,2910,
%T A335743 3019,3009,3018,3027,3028,3008,3029,3007,3036,3037,3017,3038,3016,
%U A335743 3039,3006,3045,3046,3026,3047,3025,3048,3015,3049,3005,3054,3055,3035,3056,3034,3057,3024,3058,3014,3059,3004,3063
%N A335743 Keep the first two digits of a(n) and insert a dot between them; this is now the arithmetic mean (truncated after the first decimal) of the digits used so far in the sequence. Lexicographically earliest sequence of distinct positive terms with this property.
%C A335743 The sequence starts with a(1) = 45 as any a(1) < 45 would not produce an infinite sequence.
%e A335743 a(1) = 45; inserting a dot between the first two digits produces 4.5; this is now the arithmetic mean (AM) of the digits used so far in the sequence as (4 + 5)/2 = 9/2 = 4.5 (and 4.5 is 45 with a dot);
%e A335743 a(2) = 30; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far in the sequence as (4 + 5 + 3 + 0)/4 = 12/4 = 3 (and 3 is 30 with a dot);
%e A335743 a(3) = 38; inserting a dot between the first two digits produces 3.8; this is the AM of the digits used so far (when truncated after the first decimal) as (4 + 5 + 3 + 0 + 3 + 8)/6 = 23/6 = 3.83333... which produces 38, and 3.8 is 38 with a dot);
%e A335743 a(4) = 301; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far as (4 + 5 + 3 + 0 + 3 + 8 + 3 + 0 + 1)/9 = 27/9 = 3 [and 3 is 30 with a dot, this 30 being formed by the first two digits of a(4)];
%e A335743 a(5) = 306; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far as (4 + 5 + 3 + 0 + 3 + 8 + 3 + 0 + 1 + 3 + 0 + 6)/12 = 36/12 = 3 (and 3 is 30 with a dot, this 30 being formed by the first two digits of a(5)]);
%e A335743 a(6) = 307; inserting a dot between the first two digits produces 3.0; this is the AM of the digits used so far (truncated after the first decimal) as (4 + 5 + 3 + 0 + 3 + 8 + 3 + 0 + 1 + 3 + 0 + 6 + 3 + 0 + 7)/15 = 46/15 = 3.0666... which produces 30, this 30 being formed by the first two digits of a(6)]; etc.
%Y A335743 Cf. A061383 (arithmetic mean of digits is an integer).
%K A335743 base,nonn
%O A335743 1,1
%A A335743 _Eric Angelini_ and _Carole Dubois_, Jul 02 2020