

A194100


Natural interspersion of A194126; a rectangular array, by antidiagonals.


5



1, 6, 2, 13, 7, 3, 23, 14, 8, 4, 36, 24, 15, 9, 5, 51, 37, 25, 16, 10, 11, 69, 52, 38, 26, 17, 18, 12, 89, 70, 53, 39, 27, 28, 19, 20, 112, 90, 71, 54, 40, 41, 29, 30, 21, 138, 113, 91, 72, 55, 56, 42, 43, 31, 22, 166, 139, 114, 92, 73, 74, 57, 58, 44, 32, 33, 197
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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, A194100 is a permutation of the positive integers; its inverse is A194101.


LINKS

Table of n, a(n) for n=1..67.


EXAMPLE

Northwest corner:
1...6...13...23...36
2...7...14...24...37
3...8...15...25...38
4...9...16...26...39
5...10..17...27...40
11..18..28...41...56


MATHEMATICA

z = 40; g = GoldenRatio;
c[k_] := 1 + Sum[Floor[j + j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}] (* 194126 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 800}] (* A193042 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
p = Flatten[Table[t[k, n  k + 1], {n, 1, 16}, {k, 1, n}]] (* A194100 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194101 *)


CROSSREFS

Cf. A194029, A194126, A193042, A194101.
Sequence in context: A112591 A106034 A194036 * A142867 A080977 A095951
Adjacent sequences: A194097 A194098 A194099 * A194101 A194102 A194103


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 15 2011


STATUS

approved



