

A194034


Natural interspersion of A028387, a rectangular array, by antidiagonals.


3



1, 5, 2, 11, 6, 3, 19, 12, 7, 4, 29, 20, 13, 8, 9, 41, 30, 21, 14, 15, 10, 55, 42, 31, 22, 23, 16, 17, 71, 56, 43, 32, 33, 24, 25, 18, 89, 72, 57, 44, 45, 34, 35, 26, 27, 109, 90, 73, 58, 59, 46, 47, 36, 37, 28, 131, 110, 91, 74, 75, 60, 61, 48, 49, 38, 39, 155, 132
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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, A194034 is a permutation of the positive integers; its inverse is A194035.


LINKS

Table of n, a(n) for n=1..68.


EXAMPLE

Northwest corner:
1...5...11...19...29...41
2...6...12...20...30...42
3...7...13...21...31...43
4...8...14...22...32...44
9...15..23...33...45...59


MATHEMATICA

z = 30;
c[k_] := k^2 + k  1;
c = Table[c[k], {k, 1, z}] (* A028387 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n  1]]
f = Table[f[n], {n, 1, 255}] (* A074294 *)
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, 13}, {k, 1, n}]] (* A194034 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194035 *)


CROSSREFS

Cf. A194029, A194035.
Sequence in context: A051308 A257327 A074642 * A163257 A332452 A176624
Adjacent sequences: A194031 A194032 A194033 * A194035 A194036 A194037


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Aug 12 2011


STATUS

approved



