

A348190


Positive integers where each is chosen to be the second smallest number subject to the condition that no three terms a(j), a(j+k), a(j+2*k) (for any j and k) form an arithmetic progression.


1



2, 2, 3, 2, 3, 3, 4, 2, 2, 5, 3, 4, 3, 5, 5, 7, 5, 2, 4, 2, 2, 5, 4, 6, 3, 2, 9, 5, 9, 3, 6, 10, 9, 9, 6, 5, 7, 4, 12, 11, 11, 2, 6, 4, 8, 3, 4, 6, 7, 13, 11, 5, 5, 6, 4, 8, 10, 9, 13, 4, 13, 4, 6, 6, 2, 11, 5, 4, 6, 11, 18, 9, 15, 2, 15, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The sequence seems to behave in a similar way as the "forest fire" A229037. The graph (up to n=5000) looks like it has a fractal structure, with each dense "pillar" approximately double the size of the previous one.
The terms of this sequence do not seem to be larger (on average) than those of A229037, despite the construction of this sequence.


LINKS



EXAMPLE

a(7) = 4, because 2 would form an arithmetic progression with a(1) = 2 and a(4) = 2 and 3 would form an arithmetic progression with a(5) = 3 and a(6) = 3. Therefore, 4 is the second smallest number which satisfies the condition (1 being the smallest).


PROG

(PARI) See Links section.


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



