login
A194108
Natural interspersion of A194106; a rectangular array, by antidiagonals.
5
1, 4, 2, 9, 5, 3, 15, 10, 6, 7, 23, 16, 11, 12, 8, 33, 24, 17, 18, 13, 14, 45, 34, 25, 26, 19, 20, 21, 58, 46, 35, 36, 27, 28, 29, 22, 73, 59, 47, 48, 37, 38, 39, 30, 31, 90, 74, 60, 61, 49, 50, 51, 40, 41, 32, 109, 91, 75, 76, 62, 63, 64, 52, 53, 42, 43, 129, 110
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, A194108 is a permutation of the positive integers; its inverse is A194109.
EXAMPLE
Northwest corner:
1...4...9...15...23
2...5...10..16...24
3...6...11..17...25
7...12..18..26...36
8...13..19..27...37
MATHEMATICA
z = 40; g = Sqrt[3];
c[k_] := Sum[Floor[j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}] (* A194106 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}] (* A194107 *)
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}]] (* A194108 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194109 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 15 2011
STATUS
approved