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 A194046 Natural interspersion of A052905, a rectangular array, by antidiagonals. 2
 1, 5, 2, 10, 6, 3, 16, 11, 7, 4, 23, 17, 12, 8, 9, 31, 24, 18, 13, 14, 15, 40, 32, 25, 19, 20, 21, 22, 50, 41, 33, 26, 27, 28, 29, 30, 61, 51, 42, 34, 35, 36, 37, 38, 39, 73, 62, 52, 43, 44, 45, 46, 47, 48, 49, 86, 74, 63, 53, 54, 55, 56, 57, 58, 59, 60, 100, 87, 75 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A194029 for definitions of natural fractal sequence and natural interspersion.  Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194046 is a permutation of the positive integers; its inverse is A194047. LINKS EXAMPLE Northwest corner: 1...5...10...16...23 2...6...11...17...24 3...7...12...18...25 4...8...13...19...26 9...14..20...27...35 MATHEMATICA z = 30; c[k_] := (k^2 + 5 k - 4)/2; c = Table[c[k], {k, 1, z}]  (* A052905 *) f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] f = Table[f[n], {n, 1, 255}]  (* fractal sequence [A002260] *) r[n_] := Flatten[Position[f, n]] t[n_, k_] := r[n][[k]] TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]] p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194046 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194047 *) CROSSREFS Cf. A194029, A194047 Sequence in context: A178714 A036121 A162396 * A249368 A055682 A187875 Adjacent sequences:  A194043 A194044 A194045 * A194047 A194048 A194049 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 13 2011 STATUS approved

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Last modified January 23 15:15 EST 2021. Contains 340385 sequences. (Running on oeis4.)