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A194833 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194832; an interspersion. 3
1, 2, 3, 5, 6, 4, 8, 10, 7, 9, 12, 14, 11, 13, 15, 18, 20, 16, 19, 21, 17, 24, 27, 22, 25, 28, 23, 26, 32, 35, 30, 33, 36, 31, 34, 29, 40, 44, 38, 42, 45, 39, 43, 37, 41, 49, 53, 47, 51, 55, 48, 52, 46, 50, 54, 60, 64, 57, 62, 66, 59, 63, 56, 61, 65, 58, 71, 76, 68 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

As a sequence, A194833 is a permutation of the positive integers; its inverse is A194834.

LINKS

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

EXAMPLE

Northwest corner:

1...2...5...8...12..18..24

3...6...10..14..20..27..35

4...7...11..16..22..30..38

9...13..19..25..33..42..51

15..21..28..36..45..55..66

MATHEMATICA

r = -GoldenRatio;

t[n_] := Table[FractionalPart[k*r], {k, 1, n}];

f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]

(* A194832 *)

TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]

row[n_] := Position[f, n];

u = TableForm[Table[row[n], {n, 1, 20}]]

g[n_, k_] := Part[row[n], k];

p = Flatten[Table[g[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A194833 *)

q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194834 *)

CROSSREFS

Cf. A194832, A194834.

Sequence in context: A335858 A137760 A194863 * A195108 A054077 A194872

Adjacent sequences:  A194830 A194831 A194832 * A194834 A194835 A194836

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 03 2011

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)