A097883 Triangle read by rows where T(0,0) is 1, T(m,n) = smallest as-yet-unused (reading rows from left to right) positive integer which is coprime to both T(m-1,n) and T(m-1,n-1) (or is coprime to T(m-1,0) if n=0, or to T(m-1,m-1) if n=m).

1, 2, 3, 5, 7, 4, 6, 8, 9, 11, 13, 17, 19, 10, 12, 14, 15, 16, 21, 23, 25, 27, 29, 31, 37, 20, 18, 22, 26, 28, 24, 30, 33, 41, 35, 39, 43, 45, 47, 49, 53, 32, 34, 38, 40, 36, 44, 46, 48, 50, 51, 55, 59, 61, 57, 65, 67, 63, 71, 73, 77, 52, 42, 54, 56, 58, 62, 64, 68, 74, 60, 69

Offset: 0

Author

Leroy Quet, Sep 02 2004

Keywords

• nonn
• tabl

Comments

In other words, a minimal sequence representing a square array (read by antidiagonals) in which every number is coprime to all four closest neighbors. - Ivan Neretin, Jun 05 2015

Examples

			T(3,2)=9 is smallest as-yet-unused positive integer coprime to both T(2,1)=7 and T(2,2)=4.
T(4,0)=13 is smallest as-yet-unused positive integer coprime to T(3,0)=6.
Triangle begins:
1
2, 3
5, 7, 4
6, 8, 9, 11
13,17,19,10,12
14,15,16,21,23,25
		

Links

• Ivan Neretin, Table of n, a(n) for n = 0..5049

Programs

Mathematica

a[0, 0] = 1; a[m_, n_] := a[m, n] = Block[{k = 2, p = Sort[ Flatten[ Join[ Table[ a[i, j], {i, 0, m - 1}, {j, 0, i}], Table[ a[i, j], {i, m, m}, {j, 0, n - 1}]] ]]}, While[ Position[p, k] != {} || If[n == 0, GCD[k, a[m - 1, 0]] != 1, If[n == m, GCD[k, a[m - 1, m - 1]] != 1, GCD[k, a[m - 1, n]] != 1 || GCD[k, a[m - 1, n - 1]] != 1]], k++ ]; k]; Flatten[ Table[ a[m, n], {m, 0, 10}, {n, 0, m}]] (* Robert G. Wilson v, Sep 04 2004 *)

Extensions

More terms from Robert G. Wilson v, Sep 04 2004