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A082006 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. 0
1, 2, 4, 3, 5, 7, 9, 11, 13, 19, 17, 21, 8, 23, 31, 25, 27, 29, 37, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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, May 06 2006
From Alois P. Heinz, Oct 06 2009: (Start)
T(6,1) is undefined, so there are no further terms.
For T(6,1) would be == 3 (mod 6) w.r.t. antidiagonal 6, (T(6,1)+159=6k) and it would be == 1 or == 5 (mod 6) w.r.t. column 1 (coprime to 3 & 4) which is impossible, unless backtracking is allowed and earlier elements are altered. But that is not intended by the author, because "sequence contains numbers as they are entered", and it would not make a valid definition at all. (End)
LINKS
EXAMPLE
Table is
1 2 7 9 31 25
4 5 11 23 27
3 13 8 29
19 21 37
17 41
?
CROSSREFS
Sequence in context: A238980 A327143 A343313 * A277375 A232798 A155850
KEYWORD
nonn,fini,full
AUTHOR
Amarnath Murthy, Apr 05 2003
EXTENSIONS
More terms from R. J. Mathar, May 06 2006
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)