A249116 Ordered union of the sets {h^6, h >=1} and {32*k^6, k >=1}.

1, 32, 64, 729, 2048, 4096, 15625, 23328, 46656, 117649, 131072, 262144, 500000, 531441, 1000000, 1492992, 1771561, 2985984, 3764768, 4826809, 7529536, 8388608, 11390625, 16777216, 17006112, 24137569, 32000000, 34012224, 47045881, 56689952, 64000000

Offset

1,2

Comments

Let S = {h^6, h >=1} and T = {32*k^6, k >=1}. Then S and T are disjoint. The position of n^6 in the ordered union of S and T is A249117(n), and the position of 32*n^6 is A249118(n). Equivalently, the latter two give the positions of n*2^(2/3) and n*2^(3/2), respectively, when all the numbers h*2^(2/3) and k*2^(3/2) are jointly ranked.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

{h^6, h >=1} = {1, 64, 729, 4096, 15625, 46656, 117649, ...};
{32*k^6, k >=1} = {32, 2048, 23328, 131072, 500000, ...};
so the union is {1, 32, 64, 729, 2048, 4096, 15625, ...}

Mathematica

z = 200; s = Table[h^6, {h, 1, z}]; t = Table[32*k^6, {k, 1, z}];
v = Union[s, t]  (* A249116 *)
Flatten[Table[Flatten[Position[v, s[[n]]]], {n, 1, 100}]]  (* A249117 *)
Flatten[Table[Flatten[Position[v, t[[n]]]], {n, 1, 100}]]  (* A249118 *)

Crossrefs

Cf. A249117, A249118.

Sequence in context: A358250 A235057 A339358 * A110562 A275187 A045048

Adjacent sequences: A249113 A249114 A249115 * A249117 A249118 A249119

Keyword

nonn,easy

Author

Clark Kimberling, Oct 21 2014

Status

approved