A381629 Lexicographically earliest sequence of positive integers such that no subsequence of terms at indices in arithmetic progression form an arithmetic progression in any order.

1, 1, 2, 1, 1, 2, 2, 4, 4, 1, 1, 2, 1, 1, 2, 2, 4, 4, 2, 4, 4, 5, 5, 8, 5, 5, 9, 9, 4, 2, 5, 11, 2, 2, 4, 1, 1, 5, 1, 1, 10, 2, 2, 4, 1, 1, 4, 4, 10, 10, 4, 10, 10, 12, 2, 4, 1, 2, 5, 4, 5, 10, 4, 2, 8, 2, 10, 5, 5, 10, 5, 13, 12, 13, 2, 5, 10, 5, 10, 10, 13, 5

Offset

1,3

Comments

First differs from A361933 at a(52).

This is a variant of A361933 generalized to arithmetic progressions of any nontrivial length (3 or greater).

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..1000

Example

a(52) cannot be values 1-7 without creating an arithmetic progression. a(52) cannot be 8 because the terms at i = 22,32,42,52 (common difference 10) would have the terms 5,11,2,8, which, rearranged, form the progression 2,5,8,11 (common difference 3). a(52) cannot be 9 because the terms at i = 38,45,52 (common difference 7) would have the terms 5,1,9, which in the order 1,5,9 form an arithmetic progression (common difference 4). So a(52) = 10.

Crossrefs

Cf. A361933.

Sequence in context: A309890 A229037 A361933 * A036863 A393164 A209270

Adjacent sequences: A381626 A381627 A381628 * A381630 A381631 A381632

Keyword

nonn

Author

Neal Gersh Tolunsky, Mar 29 2025

Status

approved