A335744 Insert a dot after the first digit of a(n); this is now the beginning of the arithmetic mean of the digits used so far in the sequence. Lexicographically earliest sequence of distinct positive terms with this property.

45, 30, 38, 311, 316, 326, 31, 305, 357692, 36, 37, 384, 39, 390243, 390, 376000, 386, 394, 409677, 40, 4088, 407, 4066, 4037, 40476, 4068, 4076, 40309, 40686, 4056, 4027, 40086, 402479, 40396, 40458, 4007, 397222222, 4019867

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..38.

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 beginning of the AM of the digits used so far as (4 + 5 + 3 + 0 + 3 + 8)/6 = 23/6 = 3.83333...
a(4) = 311; inserting a dot between the first two digits produces 3.11; this is the beginning of the AM of the digits used so far as (4 + 5 + 3 + 0 + 3 + 8 + 3 + 1 + 1)/9 = 28/9 = 3.111... [a(4)is not 31 as the AM would then be 3,375; a(4) is not 3111 as 311 comes lexicographically before 3111];

Crossrefs

Cf. A335743 (same idea, but the AM is given by the first two digits of a(n), separated by a dot).

Sequence in context: A196093 A196090 A335743 * A165248 A085518 A087083

Adjacent sequences: A335741 A335742 A335743 * A335745 A335746 A335747

Keyword

base,nonn

Author

Carole Dubois and Eric Angelini, Jul 02 2020

Status

approved