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 A194064 Natural interspersion of A006578; a rectangular array, by antidiagonals. 3
 1, 4, 2, 8, 5, 3, 14, 9, 6, 7, 21, 15, 10, 11, 12, 30, 22, 16, 17, 18, 13, 40, 31, 23, 24, 25, 19, 20, 52, 41, 32, 33, 34, 26, 27, 28, 65, 53, 42, 43, 44, 35, 36, 37, 29, 80, 66, 54, 55, 56, 45, 46, 47, 38, 39, 96, 81, 67, 68, 69, 57, 58, 59, 48, 49, 50 (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, A194064 is a permutation of the positive integers; its inverse is A194065. LINKS EXAMPLE Northwest corner: 1...4...8...14...21...30 2...5...9...15...22...31 3...6...10..16...23...32 7...11..17..24...33...43 12..18..25..34...44...56 MATHEMATICA z = 50; c[k_] := k (k + 1)/2 + Floor[(k^2)/4]; c = Table[c[k], {k, 1, z}]  (* A006578 *) f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] f = Table[f[n], {n, 1, 400}]   (* A194063 *) 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, 11}, {k, 1, n}]] (* A194064 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]]  (* A194065 *) CROSSREFS Cf. A194029, A194063, A194065. Sequence in context: A261830 A194038 A131819 * A194054 A191536 A187076 Adjacent sequences:  A194061 A194062 A194063 * A194065 A194066 A194067 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 14 2011 STATUS approved

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Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)