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A194104 Natural interspersion of A194102; a rectangular array, by antidiagonals. 4
1, 3, 2, 7, 4, 5, 12, 8, 9, 6, 19, 13, 14, 10, 11, 27, 20, 21, 15, 16, 17, 36, 28, 29, 22, 23, 24, 18, 47, 37, 38, 30, 31, 32, 25, 26, 59, 48, 49, 39, 40, 41, 33, 34, 35, 73, 60, 61, 50, 51, 52, 42, 43, 44, 45, 88, 74, 75, 62, 63, 64, 53, 54, 55, 56, 46, 104, 89, 90 (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, A194100 is a permutation of the positive integers; its inverse is A194101.

LINKS

Table of n, a(n) for n=1..69.

EXAMPLE

Northwest corner:

1...3...7...12...19

2...4...8...13...20

5...9...14..21...29

6...10..15..22...30

11..16..23..31...40

MATHEMATICA

z = 40; g = Sqrt[2];

c[k_] := Sum[Floor[j*g], {j, 1, k}];

c = Table[c[k], {k, 1, z}]  (* A194102 *)

f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]

f = Table[f[n], {n, 1, 800}]  (* A194103  new *)

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}]]  (* A194104 *)

q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194105 *)

CROSSREFS

Cf. A194029, A194102, A194103, A194105.

Sequence in context: A153154 A154438 A194071 * A277679 A108644 A194011

Adjacent sequences:  A194101 A194102 A194103 * A194105 A194106 A194107

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 15 2011

STATUS

approved

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Last modified July 13 15:18 EDT 2020. Contains 335688 sequences. (Running on oeis4.)