A194977 Interspersion fractally induced by A194976, a rectangular array, by antidiagonals.

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

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: A367306 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