

A098284


Minimal triangular arrangement of natural numbers such that each number has only coprime neighbors.


3



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, 43, 18, 22, 39, 47, 15, 53, 33, 49, 45, 51, 59, 20, 61, 26, 67, 32, 71, 28, 38, 55, 57, 73, 63, 79, 65, 69, 83, 75, 77, 81, 34, 89, 40, 97, 24, 101, 44, 91, 30, 36, 85, 103, 87, 107
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OFFSET

1,2


COMMENTS

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),{(n1,k+1),(n+1,k1)}) for 1<k<n;
disregarding the triangular structure the sequence is a permutation of the natural numbers with inverse A098286;


LINKS



FORMULA

Let N(n, k), the neighborhood of (n, k), be defined as:
N(1, 1)={(2, 1), (2, 2)},
N(n, 1)={(n1, 1), (n, 2), (n+1, 2), (n+1, 1)} n>1,
N(n, k)={(n1, k1), (n1, k), (n, k+1), (n+1, k+1), (n+1, k), (n, k1)}, 1<k<n
N(n, n)={(n1, n1), (n, n1), (n+1, n), (n+1, n+1)} n>1:
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)}.


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KEYWORD



AUTHOR



STATUS

approved



