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A088643
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Triangle read by rows: row n >= 1 is obtained as follows. Start with n, next term is always largest number m with 1 <= m < n which has not yet appeared in that row and such that m + previous term in the row is a prime. Stop when no further m can be found.
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9
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1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 2, 3, 4, 1, 6, 5, 2, 3, 4, 1, 7, 6, 5, 2, 3, 4, 1, 8, 5, 6, 7, 4, 3, 2, 1, 9, 8, 5, 6, 7, 4, 3, 2, 1, 10, 9, 8, 5, 6, 7, 4, 3, 2, 1, 11, 8, 9, 10, 7, 6, 5, 2, 3, 4, 1, 12, 11, 8, 9, 10, 7, 6, 5, 2, 3, 4, 1, 13, 10, 9, 8, 11, 12, 7, 6, 5, 2, 3, 4, 1, 14, 9, 10, 13, 6, 11, 12
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| It is conjectured that row n is always a permutation of {1..n}. This has been verified for n <= 400000.
Presumably many of the rows, when read from right to left, match the infinite sequence A055265.
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REFERENCES
| J. W. Roche, Letter regarding "M. J. Kenney and S. J. Bezuszka, Calendar problem 12, 1997", Mathematics Teacher, 91 (1998), 155.
F. W. Roush and D. G. Rogers, A prime algorithm?, preprint, 1999.
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EXAMPLE
| For example, the 20-th row is 20, 17, 14, 15, 16, 13, 18, 19, 12, 11, 8, 9, 10, 7, 6, 5, 2, 3, 4, 1.
Triangle begins:
1
2 1
3 2 1
4 3 2 1
5 2 3 4 1
6 5 2 3 4 1
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CROSSREFS
| A088631 and A088861 give second and third columns. Cf. A049476, A049477, A049478.
Sequence in context: A141672 A141671 A194856 * A194877 A102482 A194908
Adjacent sequences: A088640 A088641 A088642 * A088644 A088645 A088646
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KEYWORD
| nonn,tabl,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Aug 16 2005
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