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A366574
a(1) = 1; for n > 1, a(n) is the maximum positive k such that all terms a(t), a(t-m), a(t-2*m), ..., a(t-(k-1)*m), for 0<t<n and any m>=1, are equal.
2
1, 1, 2, 1, 2, 2, 2, 3, 1, 2, 3, 2, 3, 2, 3, 3, 3, 4, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 5, 1, 2, 3, 4, 5, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 6, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 3, 4, 5, 6, 3, 4, 5, 6, 3, 4, 5, 6, 4
OFFSET
1,3
COMMENTS
The terms form quickly form a repetitive pattern of arithmetic progressions of increasing length, see the graph. This leads to any given value t eventually being in a progression of length t+1 which then never increases.
See A366724 for the index where a number first appears.
LINKS
EXAMPLE
a(3) = 2 as a(2) = 1 and a(2) = a(1) = 1.
a(11) = 3 as a(10) = 2 and a(7) = a(6) = a(5) = 2.
a(18) = 4 as a(17) = 3 and a(17) = a(15) = a(13) = a(11) = 3.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Oct 13 2023
STATUS
approved