A373010 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-2*q, p-q, where q >= 0.

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

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 (3,1,2) and other progressions of the form p, p-2*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 first 200000 terms.

Formula

a(n)=1 iff n in A003278.

Crossrefs

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

Sequence in context: A373052 A268811 A371457 * A373111 A351192 A306460

Adjacent sequences: A373007 A373008 A373009 * A373012 A373013 A373014

Keyword

nonn

Author

Neal Gersh Tolunsky, May 22 2024

Status

approved