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 A194030 Natural interspersion of the Fibonacci sequence (1,2,3,5,8,...), a rectangular array, by antidiagonals. 3
 1, 2, 4, 3, 6, 7, 5, 9, 10, 11, 8, 14, 15, 16, 12, 13, 22, 23, 24, 17, 18, 21, 35, 36, 37, 25, 26, 19, 34, 56, 57, 58, 38, 39, 27, 20, 55, 90, 91, 92, 59, 60, 40, 28, 29, 89, 145, 146, 147, 93, 94, 61, 41, 42, 30, 144, 234, 235, 236, 148, 149, 95, 62, 63, 43, 31 (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, A194030 is a permutation of the positive integers; its inverse is A194031. LINKS EXAMPLE Northwest corner: 1...2...3...5...8...13 4...6...9...14..22..35 7...10..15..23..36..57 11..16..24..37..58..92 12..17..25..38..59..93 MATHEMATICA z = 40; c[k_] := Fibonacci[k + 1]; c = Table[c[k], {k, 1, z}]  (* A000045 *) f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] f = Table[f[n], {n, 1, 800}]  (* A194029 *) r[n_] := Flatten[Position[f, n]] t[n_, k_] := r[n][[k]] TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]] p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194030 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194031 *) CROSSREFS Cf. A194029, A194031. Sequence in context: A297551 A297673 A083050 * A083044 A126714 A035506 Adjacent sequences:  A194027 A194028 A194029 * A194031 A194032 A194033 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 12 2011 STATUS approved

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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)