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A057059
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Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; ... Define i(m) and j(m) by R(i(m),j(m)) = m. Then a(n) = j(A057027(n)).
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2
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1, 2, 1, 3, 1, 2, 4, 1, 3, 2, 5, 1, 4, 2, 3, 6, 1, 5, 2, 4, 3, 7, 1, 6, 2, 5, 3, 4, 8, 1, 7, 2, 6, 3, 5, 4, 9, 1, 8, 2, 7, 3, 6, 4, 5, 10, 1, 9, 2, 8, 3, 7, 4, 6, 5, 11, 1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 12, 1, 11, 2, 10, 3, 9, 4, 8, 5, 7, 6, 13, 1, 12, 2, 11, 3, 10
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Since A057027 is a permutation of the natural numbers, every natural number occurs in this sequence infinitely many times.
Triangle of spiral permutations. In the Saclolo reference sigma_n(x) is called a spiral permutation. - Michael Somos Apr 21 2011
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LINKS
| M. P. Saclolo, How a Medieval Troubadour Became a Mathematical Figure see p. 684 Equation (1)
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FORMULA
| T(n, k) = k / 2 if k is even, n - (k - 1) / 2 if k is odd where 0 < k <= n are integers. - Michael Somos Apr 21 2011
(Conjecture) Define the Chebyshev polynomials of the second kind by U_0(t) = 1, U_1(t) = 2*t, and U_r(t) = 2*t*U_(r-1)(t) - U_(r-2)(t) (r>1). Then T(n,k) = sum[j=1,...,n, U_(k-1)(cos((2*j-1)*Pi/(2*n+1)))], 1<=k<=n. - L. Edson Jeffery, Jan 09 2012
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EXAMPLE
| [1]; [2, 1]; [3, 1, 2]; [4, 1, 3, 2]; [5, 1, 4, 2, 3]; [6, 1, 5, 2, 4, 3]; ...
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PROG
| (PARI) {T(n, k) = if( k<1 | k>n, 0, if( k%2, n - (k - 1) / 2, k / 2))} /* Michael Somos Apr 21 2011 */
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CROSSREFS
| Cf. A057058; related to A141419.
Sequence in context: A089384 A144113 A165416 * A169896 A162306 A027750
Adjacent sequences: A057056 A057057 A057058 * A057060 A057061 A057062
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jul 30 2000
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