A362815 - OEIS

%I #21 Sep 28 2024 07:39:17

%S 2,3,5,6,7,11,13,14,16,17,18,19,21,22,23,25,28,29,31,37,38,39,41,43,

%T 46,47,50,51,52,53,55,58,59,61,62,64,66,67,68,70,71,73,75,77,79,82,83,

%U 85,86,88,89,93,94,96,97,99,101,103,106,107,109,110,113,115

%N Start with 2. Then, numbers are added to the sequence if they do not form any arithmetic progression p with numbers in the sequence such that length(p) > min(p).

%C All primes are in the sequence.

%C Does the density of numbers in this sequence approach 0.5?

%H Samuel Harkness, <a href="/A362815/b362815.txt">Table of n, a(n) for n = 1..10000</a>

%H Samuel Harkness, <a href="/A362815/a362815.m.txt">MATLAB program</a>

%e 2 is in the sequence.

%e For 3: the only arithmetic progression made with 3 is p = {2,3}. Here, length(p) = min(p), so 3 is a term.

%e For 4: p = {2,3,4} can be made. Here, length(p) > min(p), so 4 is not a term.

%e For 5: the only arithmetic progressions made with 5 are p = {2,5} and p = {3,5}. Neither of these have length(p) > min(p), so 5 is a term.

%e ...

%e For 9: p = {3,5,7,9} can be made. Here, length(p) > min(p), so 9 is not a term.

%o (MATLAB) See Links section.

%Y Cf. A362816, A363011.

%K nonn

%O 1,1

%A _Samuel Harkness_, May 04 2023