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.

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

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, Table of n, a(n) for n = 1..8000

Rémy Sigrist, PARI program for A348190

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

Adjacent sequences: A348187 A348188 A348189 * A348191 A348192 A348193

Keyword

nonn,look

Author

Albert Böschow, Oct 06 2021

Status

approved