A097883 - OEIS

%I #16 Jun 24 2015 18:57:15

%S 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,

%T 18,22,26,28,24,30,33,41,35,39,43,45,47,49,53,32,34,38,40,36,44,46,48,

%U 50,51,55,59,61,57,65,67,63,71,73,77,52,42,54,56,58,62,64,68,74,60,69

%N 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).

%C 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

%H Ivan Neretin, <a href="/A097883/b097883.txt">Table of n, a(n) for n = 0..5049</a>

%e T(3,2)=9 is smallest as-yet-unused positive integer coprime to both T(2,1)=7 and T(2,2)=4.

%e T(4,0)=13 is smallest as-yet-unused positive integer coprime to T(3,0)=6.

%e Triangle begins:

%e 1

%e 2, 3

%e 5, 7, 4

%e 6, 8, 9, 11

%e 13,17,19,10,12

%e 14,15,16,21,23,25

%t 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 *)

%K nonn,tabl

%O 0,2

%A _Leroy Quet_, Sep 02 2004

%E More terms from _Robert G. Wilson v_, Sep 04 2004