A129258 A prime separator array.

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.

Links

Table of n, a(n) for n=1..69.

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

Cf. A129259, A129260.

Sequence in context: A345252 A361927 A360633 * A256988 A104650 A083179

Adjacent sequences: A129255 A129256 A129257 * A129259 A129260 A129261

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 06 2007

Status

approved