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A194969 Interspersion fractally induced by A194968, a rectangular array, by antidiagonals. 4
1, 2, 3, 4, 6, 5, 7, 10, 8, 9, 11, 15, 12, 13, 14, 16, 21, 17, 18, 20, 19, 22, 28, 23, 24, 27, 25, 26, 29, 36, 30, 31, 35, 32, 34, 33, 37, 45, 38, 39, 44, 40, 43, 41, 42, 46, 55, 47, 48, 54, 49, 53, 50, 51, 52, 56, 66, 57, 58, 65, 59, 64, 60, 61, 63, 62, 67, 78, 68 (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, A194969 is a permutation of the positive integers, with inverse A194970.

LINKS

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

EXAMPLE

Northwest corner:

1...2...4...7...11..16

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

5...8...12..17..23..30

9...13..18..24..31..39

14..20..27..35..44..54

MATHEMATICA

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

Table[p[n], {n, 1, 90}]  (* A019446 *)

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]  (* A194968 *)

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}]]  (* A194969 *)

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

{n, 1, 80}]]  (* A194970 *)

CROSSREFS

Cf. A194958, A019446, A194968, A194970.

Sequence in context: A194970 A194982 A064578 * A194981 A057027 A090894

Adjacent sequences:  A194966 A194967 A194968 * A194970 A194971 A194972

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 07 2011

STATUS

approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)