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 A194108 Natural interspersion of A194106; a rectangular array, by antidiagonals. 5
 1, 4, 2, 9, 5, 3, 15, 10, 6, 7, 23, 16, 11, 12, 8, 33, 24, 17, 18, 13, 14, 45, 34, 25, 26, 19, 20, 21, 58, 46, 35, 36, 27, 28, 29, 22, 73, 59, 47, 48, 37, 38, 39, 30, 31, 90, 74, 60, 61, 49, 50, 51, 40, 41, 32, 109, 91, 75, 76, 62, 63, 64, 52, 53, 42, 43, 129, 110 (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, A194108 is a permutation of the positive integers; its inverse is A194109. LINKS EXAMPLE Northwest corner: 1...4...9...15...23 2...5...10..16...24 3...6...11..17...25 7...12..18..26...36 8...13..19..27...37 MATHEMATICA z = 40; g = Sqrt[3]; c[k_] := Sum[Floor[j*g], {j, 1, k}]; c = Table[c[k], {k, 1, z}]  (* A194106 *) f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]] f = Table[f[n], {n, 1, 800}]  (* A194107 *) 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, 16}, {k, 1, n}]]  (* A194108 *) q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194109 *) CROSSREFS Cf. A194029, A194106, A194107, A194109. Sequence in context: A262025 A118013 A157647 * A091452 A194032 A191739 Adjacent sequences:  A194105 A194106 A194107 * A194109 A194110 A194111 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 15 2011 STATUS approved

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)