A373111 Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form a progression of the form c, c+2d, c+d, where d >= 0.

1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 3, 1, 1, 4, 4, 3, 2, 3, 3, 4, 4, 5, 4, 4, 5, 5, 1, 1, 4, 1, 1, 5, 5, 6, 5, 1, 1, 6, 1, 1, 2, 2, 5, 2, 2, 5, 6, 6, 7, 2, 2, 7, 2, 2, 8, 7, 6, 5, 6, 8, 8, 9, 5, 6, 9, 8, 9, 2, 2, 7, 3, 2, 8, 2, 3, 8, 7, 3, 7, 4, 1, 1, 6, 1, 1, 9, 8

Offset: 1

Author

Neal Gersh Tolunsky, May 25 2024

Keywords

• nonn

Comments

This sequence avoids one of the six permutations of a set of three integers in arithmetic progression. For example, the set {1,2,3} can be ordered as tuples (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). In this sequence, we avoid (1,3,2) and other progressions of the form c, c+2d, c+d, for all d >= 0.

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
• Neal Gersh Tolunsky, Graph of first 200000 terms.

Crossrefs

Cf. A229037, A373010, A100480, A309890, A373052, A361933, A371632, A371457.

Formula

a(n)=1 iff n in A003278.