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 A194034 Natural interspersion of A028387, a rectangular array, by antidiagonals. 3
 1, 5, 2, 11, 6, 3, 19, 12, 7, 4, 29, 20, 13, 8, 9, 41, 30, 21, 14, 15, 10, 55, 42, 31, 22, 23, 16, 17, 71, 56, 43, 32, 33, 24, 25, 18, 89, 72, 57, 44, 45, 34, 35, 26, 27, 109, 90, 73, 58, 59, 46, 47, 36, 37, 28, 131, 110, 91, 74, 75, 60, 61, 48, 49, 38, 39, 155, 132 (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, A194034 is a permutation of the positive integers; its inverse is A194035. LINKS EXAMPLE Northwest corner: 1...5...11...19...29...41 2...6...12...20...30...42 3...7...13...21...31...43 4...8...14...22...32...44 9...15..23...33...45...59 MATHEMATICA z = 30; c[k_] := k^2 + k - 1; c = Table[c[k], {k, 1, z}]  (* A028387 *) f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] f = Table[f[n], {n, 1, 255}]  (* A074294 *) 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}]]  (* A194034 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194035 *) CROSSREFS Cf. A194029, A194035. Sequence in context: A051308 A257327 A074642 * A163257 A332452 A176624 Adjacent sequences:  A194031 A194032 A194033 * A194035 A194036 A194037 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 12 2011 STATUS approved

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Last modified May 18 05:31 EDT 2022. Contains 353783 sequences. (Running on oeis4.)