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 A259280 a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings of length greater than 1. 7
 1, 2, 4, 5, 7, 9, 11, 14, 16, 19, 21, 24, 27, 30, 33, 36, 40, 43, 47, 50, 54, 57, 61, 65, 69, 73, 77, 81, 85, 90, 94, 99, 103, 108, 112, 117, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 172, 177, 183, 188, 194, 199, 205, 210, 216, 221, 227, 233, 239, 245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The lexicographically earliest positive integer sequence with no duplicate substrings is [1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, ...]. Note: Trivial substring of length 1 are allowed to recur, i.e., duplicate terms are permitted. Non-examples of positive integer sequences with no duplicate substrings are [1, 1, 1] (the substring [1, 1] occurs twice) and [1, 2, 3, 1, 2] (the substring [1, 2] occurs twice). LINKS Peter Kagey, Table of n, a(n) for n = 1..10000 FORMULA a(1) = 1, a(n) = ceiling((n + 1 + A060432(n - 1))/2) for n > 1. EXAMPLE Lexicographically earliest examples: a(1) = 1 via [1] a(2) = 2 via [1, 1] a(3) = 4 via [1, 1, 2] a(4) = 5 via [1, 1, 2, 1] a(5) = 7 via [1, 1, 2, 2, 1] a(6) = 9 via [1, 1, 2, 1, 3, 1] a(7) = 11 via [1, 1, 2, 2, 1, 3, 1] a(8) = 14 via [1, 1, 2, 1, 3, 1, 4, 1] a(9) = 16 via [1, 1, 2, 1, 3, 2, 2, 3, 1] a(10) = 19 via [1, 1, 2, 1, 3, 2, 2, 3, 3, 1] a(11) = 21 via [1, 1, 2, 1, 3, 2, 2, 3, 1, 4, 1] a(12) = 24 via [1, 1, 2, 1, 3, 2, 2, 3, 3, 1, 4, 1] a(13) = 27 via [1, 1, 2, 1, 3, 1, 4, 2, 2, 3, 2, 4, 1] PROG (Ruby) def a259280(n) lower_bound = 0.5 * (a060432(n - 1) + n + 1) lower_bound.ceil end CROSSREFS Sequence in context: A258049 A057352 A156625 * A186388 A058577 A356075 Adjacent sequences: A259277 A259278 A259279 * A259281 A259282 A259283 KEYWORD nonn AUTHOR Peter Kagey, Nov 30 2015 STATUS approved

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Last modified September 15 02:47 EDT 2024. Contains 375930 sequences. (Running on oeis4.)