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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.
3
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, Graph of the first 200000 terms
FORMULA
a(n)=1 iff n in A003278.
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Jun 01 2024
STATUS
approved