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A194075
Natural interspersion of A194073; a rectangular array, by antidiagonals.
4
1, 4, 2, 7, 5, 3, 13, 8, 6, 10, 19, 14, 9, 16, 11, 28, 20, 15, 22, 17, 12, 37, 29, 21, 31, 23, 18, 25, 49, 38, 30, 40, 32, 24, 34, 26, 61, 50, 39, 52, 41, 33, 43, 35, 27, 76, 62, 51, 64, 53, 42, 55, 44, 36, 46, 91, 77, 63, 79, 65, 54, 67, 56, 45, 58, 47, 109, 92, 78
OFFSET
1,2
COMMENTS
See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194075 is a permutation of the positive integers; its inverse is A194076.
EXAMPLE
Northwest corner:
1...4...7...13...19
2...5...8...14...20
3...6...9...15...21
10..16..22..31...40
11..17..23..32...41
MATHEMATICA
z = 70;
c[k_] := 1 + Floor[(3/4) k^2];
c = Table[c[k], {k, 1, z}] (* A194073 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}] (* A194074 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[
Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194075 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 90}]] (* A194076 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 14 2011
STATUS
approved