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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
Neal Gersh Tolunsky, Scatterplot for n=1...8000
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
Cf. A229037.
Sequence in context: A217865 A185166 A276555 * A211100 A329326 A105264
KEYWORD
nonn,look
AUTHOR
Albert Böschow, Oct 06 2021
STATUS
approved

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Last modified May 26 15:05 EDT 2024. Contains 372826 sequences. (Running on oeis4.)