A371457 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 p, p-q, p+q, where q >= 0.

1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 4, 3, 2, 6, 5, 5, 6, 3, 4, 3, 4, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 6, 4, 2, 4, 6, 8, 6, 5, 8, 4, 6, 2, 7, 5, 11, 5, 5, 7, 6, 11, 4, 9, 6, 7, 9, 7, 5, 4, 3, 8, 9, 5, 5, 8, 3, 5, 3, 3, 1, 1, 2, 1, 1, 2

Offset

1,3

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 (2,1,3) and other progressions of the form p, p-q, p+q, for all q >= 0.

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Neal Gersh Tolunsky, Graph of the first 200000 terms

Formula

a(n)=1 iff n in A003278.

Crossrefs

Cf. A229037, A100480, A373010, A309890, A371632, A373052, A373111, A361933.

Sequence in context: A100480 A373052 A268811 * A373010 A373111 A351192

Adjacent sequences: A371454 A371455 A371456 * A371458 A371459 A371460

Keyword

nonn

Author

Neal Gersh Tolunsky, Jun 01 2024

Status

approved