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 A194071 Natural interspersion of A194069; a rectangular array, by antidiagonals. 4
 1, 3, 2, 7, 4, 5, 11, 8, 9, 6, 17, 12, 13, 10, 15, 25, 18, 19, 14, 21, 16, 33, 26, 27, 20, 29, 22, 23, 43, 34, 35, 28, 37, 30, 31, 24, 55, 44, 45, 36, 47, 38, 39, 32, 41, 67, 56, 57, 46, 59, 48, 49, 40, 51, 42, 81, 68, 69, 58, 71, 60, 61, 50, 63, 52, 53, 97, 82, 83 (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, A194071 is a permutation of the positive integers; its inverse is A194072. LINKS EXAMPLE Northwest corner: 1...3...7...11...17 2...4...8...12...18 5...9...13..19...27 6...10..14..20...28 15..21..29..37...47 MATHEMATICA z = 70; c[k_] := 1 + Floor[(2/3) k^2]; c = Table[c[k], {k, 1, z}]  (* A194069 *) f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] f = Table[f[n], {n, 1, 300}]   (* A194070 *) 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, 14}, {k, 1, n}]] (* A194071 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194072 *) CROSSREFS Cf. A194029, A194069, A194070, A194072. Sequence in context: A175057 A153154 A154438 * A194104 A277679 A108644 Adjacent sequences:  A194068 A194069 A194070 * A194072 A194073 A194074 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 14 2011 STATUS approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)