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%I #12 Mar 30 2012 18:50:45
%S 1,2,3,5,7,4,6,11,9,13,17,19,8,23,10,12,25,21,29,27,31,35,37,16,41,14,
%T 43,18,22,39,47,15,53,33,49,45,51,59,20,61,26,67,32,71,28,38,55,57,73,
%U 63,79,65,69,83,75,77,81,34,89,40,97,24,101,44,91,30,36,85,103,87,107
%N Minimal triangular arrangement of natural numbers such that each number has only coprime neighbors.
%C T(n,k) = A082196(n,k) for n<=6 and k<=6, but T(7,1)=35 whereas A082196(7,1)=37, with a different neighborhood: N'(n,k) = Union(N(n,k),{(n-1,k+1),(n+1,k-1)}) for 1<k<n;
%C disregarding the triangular structure the sequence is a permutation of the natural numbers with inverse A098286;
%C A098285(n) = a(a(n)).
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F Let N(n, k), the neighborhood of (n, k), be defined as:
%F N(1, 1)={(2, 1), (2, 2)},
%F N(n, 1)={(n-1, 1), (n, 2), (n+1, 2), (n+1, 1)} n>1,
%F N(n, k)={(n-1, k-1), (n-1, k), (n, k+1), (n+1, k+1), (n+1, k), (n, k-1)}, 1<k<n
%F N(n, n)={(n-1, n-1), (n, n-1), (n+1, n), (n+1, n+1)} n>1:
%F T(n, k) = Min{x: x<>T(m, j) m<=n and x coprime to T(m, j) for (m, j) in N(n, k)}.
%K nonn,tabl
%O 1,2
%A _Reinhard Zumkeller_, Sep 02 2004
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