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.

45, 30, 38, 301, 306, 307, 305, 308, 304, 318, 303, 309, 316, 302, 2900, 2901, 2910, 3019, 3009, 3018, 3027, 3028, 3008, 3029, 3007, 3036, 3037, 3017, 3038, 3016, 3039, 3006, 3045, 3046, 3026, 3047, 3025, 3048, 3015, 3049, 3005, 3054, 3055, 3035, 3056, 3034, 3057, 3024, 3058, 3014, 3059, 3004, 3063

Offset

1,1

Comments

The sequence starts with a(1) = 45 as any a(1) < 45 would not produce an infinite sequence.

Links

Table of n, a(n) for n=1..53.

Example

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);
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);
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);
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)];
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)]);
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.

Crossrefs

Cf. A061383 (arithmetic mean of digits is an integer).

Sequence in context: A033365 A196093 A196090 * A335744 A165248 A085518

Adjacent sequences: A335740 A335741 A335742 * A335744 A335745 A335746

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jul 02 2020

Status

approved