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

1,3

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 (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.

Formula

a(n)=1 iff n in A003278.

Crossrefs

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

Sequence in context: A268811 A371457 A373010 * A351192 A306460 A317805

Adjacent sequences: A373108 A373109 A373110 * A373112 A373113 A373114

Keyword

nonn

Author

Neal Gersh Tolunsky, May 25 2024

Status

approved