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A249098 Position of n^6 in the ordered union of {h^6, h >=1} and {3*k^6, k >=1}. 3
1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 32, 34, 36, 38, 40, 42, 43, 45, 47, 49, 51, 53, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 76, 78, 80, 82, 84, 86, 87, 89, 91, 93, 95, 97, 98, 100, 102, 104, 106, 108, 109, 111, 113, 115 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let S = {h^6, h >=1} and T = {3*k^6, k >=1}.  Then S and T are disjoint, with ordered union given by A249097.  The position of n^6 is A249098(n), and the position of 3*n^6 is A249099(n).  Also, a(n) is the position of n in the joint ranking of the positive integers and the numbers k*3^(1/6), so that A249098 and A249099 are a pair of Beatty sequences.

LINKS

Table of n, a(n) for n=1..63.

FORMULA

Empirical g.f.: x*(x^6+x^5+2*x^4+2*x^3+2*x^2+2*x+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)). - Colin Barker, Oct 22 2014

EXAMPLE

{h^6, h >=1} = {1, 64, 729, 4096, 15625, 46656, 117649, ...};

{3*k^6, k >=1} = {3, 192, 2187, 12288, 46875, 139968, ...};

so the ordered union is {1, 3, 64, 192, 729, 2187, 4096, 12288, ...}, and

a(2) = 3 because 2^6 is in position 3.

MATHEMATICA

z = 200; s = Table[h^6, {h, 1, z}]; t = Table[3*k^6, {k, 1, z}]; u = Union[s, t];

v = Sort[u]  (* A249073 *)

m = Min[120, Position[v, 2*z^2]]

Flatten[Table[Flatten[Position[v, s[[n]]]], {n, 1, m}]]  (* A249098 *)

Flatten[Table[Flatten[Position[v, t[[n]]]], {n, 1, m}]]  (* A249099 *)

CROSSREFS

Cf. A249097, A249099.

Sequence in context: A184808 A329837 A214315 * A287774 A308412 A327254

Adjacent sequences:  A249095 A249096 A249097 * A249099 A249100 A249101

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 21 2014

STATUS

approved

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Last modified November 25 20:20 EST 2020. Contains 338627 sequences. (Running on oeis4.)