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A194104 Natural interspersion of A194102; a rectangular array, by antidiagonals. 4
1, 3, 2, 7, 4, 5, 12, 8, 9, 6, 19, 13, 14, 10, 11, 27, 20, 21, 15, 16, 17, 36, 28, 29, 22, 23, 24, 18, 47, 37, 38, 30, 31, 32, 25, 26, 59, 48, 49, 39, 40, 41, 33, 34, 35, 73, 60, 61, 50, 51, 52, 42, 43, 44, 45, 88, 74, 75, 62, 63, 64, 53, 54, 55, 56, 46, 104, 89, 90 (list; table; graph; refs; listen; history; text; internal format)
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
EXAMPLE
Northwest corner:
1...3...7...12...19
2...4...8...13...20
5...9...14..21...29
6...10..15..22...30
11..16..23..31...40
MATHEMATICA
z = 40; g = Sqrt[2];
c[k_] := Sum[Floor[j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}] (* A194102 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}] (* A194103 new *)
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}]] (* A194104 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194105 *)
CROSSREFS
Sequence in context: A154438 A354367 A194071 * A277679 A108644 A194011
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 15 2011
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)