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A194984 Interspersion fractally induced by A194964, a rectangular array, by antidiagonals. 5
1, 3, 2, 6, 4, 5, 10, 7, 9, 8, 15, 11, 14, 12, 13, 21, 16, 20, 17, 19, 18, 28, 22, 27, 23, 26, 24, 25, 36, 29, 35, 30, 34, 31, 33, 32, 45, 37, 44, 38, 43, 39, 42, 40, 41, 55, 46, 54, 47, 53, 48, 52, 49, 51, 50, 66, 56, 65, 57, 64, 58, 63, 59, 62, 61, 60, 78, 67, 77 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194984 is a permutation of the positive integers, with inverse A194985.

LINKS

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

EXAMPLE

Northwest corner:

1...3...6...10..15..21..28

2...4...7...11..16..22..29

5...9...14..20..27..35..44

8...12..17..23..30..38..47

13..19..26..34..43..53..64

MATHEMATICA

r = Sqrt[5]; p[n_] := 1 + Floor[n/r]

Table[p[n], {n, 1, 90}]  (* A194964 *)

g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

f[20] (* A194983 *)

row[n_] := Position[f[30], n];

u = TableForm[Table[row[n], {n, 1, 5}]]

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

w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},

{k, 1, n}]]  (* A194984 *)

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

{n, 1, 80}]]  (* A194985 *)

CROSSREFS

Cf. A194959, A194964, A194983, A194985.

Sequence in context: A066182 A195114 A059399 * A194988 A195074 A194918

Adjacent sequences:  A194981 A194982 A194983 * A194985 A194986 A194987

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 07 2011

STATUS

approved

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Last modified September 24 12:23 EDT 2021. Contains 347642 sequences. (Running on oeis4.)