

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
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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



