A098284 Minimal triangular arrangement of natural numbers such that each number has only coprime neighbors.

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

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),{(n-1,k+1),(n+1,k-1)}) for 1<k<n;

disregarding the triangular structure the sequence is a permutation of the natural numbers with inverse A098286;

A098285(n) = a(a(n)).

Links

Table of n, a(n) for n=1..71.

Index entries for sequences that are permutations of the natural numbers

Formula

Let N(n, k), the neighborhood of (n, k), be defined as:

N(1, 1)={(2, 1), (2, 2)},

N(n, 1)={(n-1, 1), (n, 2), (n+1, 2), (n+1, 1)} n>1,

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

N(n, n)={(n-1, n-1), (n, n-1), (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)}.

Crossrefs

Sequence in context: A097883 A290020 A178595 * A082196 A292876 A126049

Adjacent sequences: A098281 A098282 A098283 * A098285 A098286 A098287

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Sep 02 2004

Status

approved