A194912 - OEIS

A194912

Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.

1, 2, 3, 4, 5, 6, 8, 9, 10, 7, 12, 14, 15, 11, 13, 17, 19, 21, 16, 18, 20, 23, 25, 27, 22, 24, 26, 28, 31, 33, 35, 29, 32, 34, 36, 30, 39, 42, 44, 37, 40, 43, 45, 38, 41, 48, 51, 54, 46, 49, 52, 55, 47, 50, 53, 58, 61, 64, 56, 59, 62, 65, 57, 60, 63, 66, 70, 73, 76

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OFFSET

1,2

COMMENTS

See A194832 for a general discussion. A194912 is not equal to A194842.

LINKS

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

EXAMPLE

Northwest corner:

1...2...4...8...12..17

3...5...9...14..19..25

6...10..15..21..27..35

7...11..16..22..29..37

13..18..24..32..40..49

MATHEMATICA

r = 2^(1/3);

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

f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@

Sort[t[n], Less]], {n, 1, 20}]] (* A194911 *)

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}]] (* A194912 *)

q[n_] := Position[p, n]; Flatten[Table[q[n],

{n, 1, 80}]] (* A194913 *)

CROSSREFS

Cf. A194832, A194911, A194913.

Sequence in context: A303595 A195184 A194842 * A194866 A345254 A004726

Adjacent sequences: A194909 A194910 A194911 * A194913 A194914 A194915

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 05 2011

STATUS

approved