A362815 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).

2, 3, 5, 6, 7, 11, 13, 14, 16, 17, 18, 19, 21, 22, 23, 25, 28, 29, 31, 37, 38, 39, 41, 43, 46, 47, 50, 51, 52, 53, 55, 58, 59, 61, 62, 64, 66, 67, 68, 70, 71, 73, 75, 77, 79, 82, 83, 85, 86, 88, 89, 93, 94, 96, 97, 99, 101, 103, 106, 107, 109, 110, 113, 115

Offset

1,1

Comments

All primes are in the sequence.

Does the density of numbers in this sequence approach 0.5?

Links

Samuel Harkness, Table of n, a(n) for n = 1..10000

Samuel Harkness, MATLAB program

Example

2 is in the sequence.
For 3: the only arithmetic progression made with 3 is p = {2,3}. Here, length(p) = min(p), so 3 is a term.
For 4: p = {2,3,4} can be made. Here, length(p) > min(p), so 4 is not a term.
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.
...
For 9: p = {3,5,7,9} can be made. Here, length(p) > min(p), so 9 is not a term.

Prog

(MATLAB) See Links section.

Crossrefs

Cf. A362816, A363011.

Sequence in context: A053328 A333786 A089633 * A358772 A003172 A340856

Adjacent sequences: A362812 A362813 A362814 * A362816 A362817 A362818

Keyword

nonn

Author

Samuel Harkness, May 04 2023

Status

approved