OFFSET
1,1
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.
FORMULA
Empirical g.f.: x*(3*x^4+2*x^3+2*x^2+2*x+2) / ((x-1)^2*(x^4+x^3+x^2+x+1)). - Colin Barker, Oct 22 2014
Conjecture: a(n) = 2n + floor(n/5). - Wesley Ivan Hurt, Dec 28 2016
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) = 4 because 3*2^6 is in position 4.
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 21 2014
STATUS
approved