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Search: id:A082006
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| A082006 |
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In the following square array numbers (not occurring earlier) are entered like this: a(1, 1), a(1, 2), a(2, 1), a(3, 1), a(2, 2), a(1, 3), a(1, 4), a(2, 3), a(3, 2), a(4, 1), a(5, 1), a(4, 2), ... such that every entry is coprime to the members of the row and column it belongs, with the condition that the n-th diagonal sum is a multiple of n. 1 2 7 9 31 25... 4 5 11 23 27... 3 13 8... 19 21... 17 ... ... Sequence contains numbers as they are entered. |
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+0
5
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| 1, 2, 4, 3, 5, 7, 9, 11, 13, 19, 17, 21, 8, 23, 31, 25, 27, 29, 37, 41
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Next term T(6,1) =a(21)> 500000, a(21) is odd. The sum of the first diagonal is 1 (a multiple of 1). The sum of the second diagonal is T(1,2)+T(2,1)=2+4=6 (a multiple of 2). The sum of the 3rd diagonal is T(1,3)+T(2,2)+T(3,1)=7+5+3=15 (a multiple of 3). The sum of the 4th diagonal is T(1,4)+T(2,3)+T(3,2)+T(4,1)=9+11+13+19=52 (a multiple of 4). The members of the first row (1,2,7,9,31,25,..) are mutually coprime. The members of the 2nd row (4,5,11,23,27,..) are mutually coprime. The members of the first column (1,4,3,19,17,..) are mutually coprime. The members of the 2nd column (2,5,13,21,..) are mutually coprime. The a(n) transverses the table in meandering fashion: first diagonal up, 2nd diagonal down, 3rd diagonal up, 4th down etc. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2006
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EXAMPLE
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Table is
1 2 7 9 31 25
4 5 11 23 27
3 13 8 29
19 21 37
17 41
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CROSSREFS
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Cf. A082007, A082008, A082009, A082010.
Sequence in context: A074147 A138607 A093506 this_sequence A134464 A104472 A132193
Adjacent sequences: A082003 A082004 A082005 this_sequence A082007 A082008 A082009
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KEYWORD
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more,nonn,uned,obsc
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 05 2003
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EXTENSIONS
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Needs editing - see A082002, A082003, A082004, A082005 for a model. - njas
However, David Wasserman (dwasserm(AT)earthlink.com) has looked at this sequence, and reports that the current definition does not define the sequence, and that it is unclear how to correct it. Aug 05 2004
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2006
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