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)
EXAMPLE
Table is
1 2 7 9 31 25
4 5 11 23 27
3 13 8 29
19 21 37
17 41
?
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Amarnath Murthy, Apr 05 2003
EXTENSIONS
More terms from R. J. Mathar, May 06 2006
STATUS
approved