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Search: id:A098284
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| A098284 |
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Minimal triangular arrangement of natural numbers such that each number has only coprime neighbors. |
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+0
4
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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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)).
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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FORMULA
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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)}.
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CROSSREFS
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Adjacent sequences: A098281 A098282 A098283 this_sequence A098285 A098286 A098287
Sequence in context: A124322 A075241 A097883 this_sequence A082196 A126049 A082331
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 02 2004
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