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

Author

Neal Gersh Tolunsky, Mar 29 2025

Keywords

• nonn

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).

Examples

			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.
		

Links

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

Crossrefs

Cf. A361933.