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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.
6
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, Graph of first 200000 terms.
FORMULA
a(n)=1 iff n in A003278.
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, May 22 2024
STATUS
approved