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A194977 Interspersion fractally induced by A194976, a rectangular array, by antidiagonals. 5
1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 15, 13, 14, 16, 17, 21, 18, 19, 20, 22, 23, 28, 24, 25, 27, 26, 29, 30, 36, 31, 32, 35, 33, 34, 37, 38, 45, 39, 40, 44, 41, 42, 43, 46, 47, 55, 48, 49, 54, 50, 51, 52, 53, 56, 57, 66, 58, 59, 65, 60, 61, 62, 64, 63, 67, 68, 78, 69, 70, 77, 71, 72, 73, 76, 74, 75 (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, A194977 is a permutation of the positive integers, with inverse A194978.

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

EXAMPLE

Northwest corner:

   1  2  4  7 11 16 22

   3  5  8 12 17 23 30

   6 10 15 21 28 36 45

   9 13 18 24 31 39 48

  14 19 25 32 40 49 59

MATHEMATICA

r = Sqrt[2]; p[n_] := 1 + Floor[n/r]

Table[p[n], {n, 1, 90}]  (* A049474 *)

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] (* A194976 *)

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}]] (* A194977 *)

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

{n, 1, 80}]] (* A194978 *)

CROSSREFS

Cf. A194959, A194976, A194978.

Sequence in context: A031044 A194978 A195096 * A195083 A073294 A073295

Adjacent sequences:  A194974 A194975 A194976 * A194978 A194979 A194980

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 07 2011

EXTENSIONS

Terms a(70) and beyond from G. C. Greubel, Mar 28 2018

STATUS

approved

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Last modified August 2 03:55 EDT 2021. Contains 346409 sequences. (Running on oeis4.)