|
|
A276222
|
|
Position of n^s in the joint ranking of {h} and {k^s}, h >= 1, k >= 2, s = golden ratio = (1+sqrt(5))/2.
|
|
1
|
|
|
4, 7, 12, 17, 23, 29, 35, 42, 50, 58, 66, 75, 84, 93, 103, 113, 124, 135, 146, 157, 169, 181, 194, 206, 219, 233, 246, 260, 274, 288, 303, 318, 333, 349, 364, 380, 396, 413, 430, 446, 464, 481, 499, 517, 535, 553, 572, 590, 610, 629, 648, 668, 688, 708, 728
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n + floor(n^s), n >= 2; the complement is given by n + floor(n^(1/s)), n >= 1.
|
|
EXAMPLE
|
The first numbers in the joint ranking are
1 < 2 < 3 < 2^s < 4 < 5 < 3^s < 6 < 7 < 8 < 9 < 4^s, so that a(n) = (4,7,12,...).
|
|
MATHEMATICA
|
z = 150; s = N[GoldenRatio, 100];
u = Table[n + Floor[n^s], {n, 2, z}];
v = Table[n + Floor[n^(1/s)], {n, 1, z^s}];
w = Union[u, v]; Flatten[Table[Position[w, u[[n]]], {n, 1, z}]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|