

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.


1



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
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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



