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A129258
A prime separator array.
2
1, 2, 3, 4, 6, 5, 7, 12, 10, 8, 9, 21, 20, 16, 11, 13, 27, 35, 32, 22, 17, 15, 39, 45, 56, 44, 28, 17, 18, 45, 65, 72, 77, 56, 34, 19, 23, 54, 75, 104, 99, 98, 68, 38, 24, 25, 69, 90, 120, 143, 126, 119, 76, 48, 26, 29, 75, 115, 144, 165, 182, 153, 133, 96, 52, 30, 31, 87, 125
OFFSET
1,2
COMMENTS
Every prime is in row 1 or column 1 but not both. Row 1, A129259, contains the primes 2,7,13,23,29,31. Column 1, A129260, contains the primes 3,5,11,17,19,37. The determinant of every 2 X 2 submatrix is zero. T(n,1)>T(1,n) for n>=2; is T(n,1)=T(1,n)+1 for infinitely many n? Every positive integer occurs in the array, some more than once.
FORMULA
T(1,1)=1. For n>=1, let S(n)={(i,j): 1<=i<=n and 1<=j<=n}. Once T(i,j) is defined on S(n), define T(1,n+1)=least positive integer (l.p.i.) not among T(i,j) for (i,j) in S(n); T(n+1,1)=l.p.i. not among T(i,j) for (i,j) in S(n) and not T(1,n+1); T(m,n+1)=T(m,1)*T(1,n+1) for m=2,3,...,n+1; T(n+1,m)=T(n+1,1)*T(1,m) for m=2,3,...,n+1.
EXAMPLE
Northwest corner:
1 2 4 7 9 13 15 18
3 6 12 21 27 39 45 54
5 10 20 35 45 65 75 90
8 16 32 56 72 104 120 144
11 22 44 77 99 143 165 198
CROSSREFS
Sequence in context: A374818 A361927 A360633 * A256988 A104650 A083179
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Apr 06 2007
STATUS
approved