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A226239
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Minimum m such that there exists an n-row subtractive triangle with distinct integers in 1..m.
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1
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1, 3, 6, 10, 15, 22, 33, 44, 59, 76, 101, 125, 158
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OFFSET
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1,2
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COMMENTS
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In an n-row subtractive triangle, there are n-i+1 integers in the i-th row. The integers in the first row are arbitrary. From the next row, the integers are the absolute difference between adjacent integers in the previous row.
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LINKS
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Table of n, a(n) for n=1..13.
Chyanog, A Chinese web page where the problem was posed.
International Mathematical Olympiad, Problem 3 of IMO 2018.
Denis Cazor, Algorithme en Français
Denis Cazor, Algorithm in English
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EXAMPLE
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a(6)=22 because there is a 6-row subtractive triangle with distinct integers in [1..22] as follows:
1: 6 20 22 3 21 13
2: 14 2 19 18 8
3: 12 17 1 10
4: 5 16 9
5: 11 7
6: 4
However, there is no such triangle with distinct integers in [1..21].
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CROSSREFS
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Cf. A035312, A035313.
Sequence in context: A177100 A265071 A330910 * A209231 A137358 A143963
Adjacent sequences: A226236 A226237 A226238 * A226240 A226241 A226242
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KEYWORD
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nonn,hard,more
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AUTHOR
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Yi Yang, Jun 01 2013
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EXTENSIONS
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a(12) from Yi Yang, Mar 04 2015
a(13) from Denis Cazor, Aug 01 2022
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STATUS
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approved
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