OFFSET
1,1
COMMENTS
This is the third of four sequences, u^v, u^v', u'^v, u'^v', that partition the positive integers. See A346308.
EXAMPLE
(1) u ^ v = ( 1, 5, 8, 12, 15, 19, 22, 24, 25, 29, 31, 32, ...) = A346308
(2) u ^ v' = ( 2, 4, 7, 9, 11, 14, 16, 18, 21, 26, 28, 33, ...) = A356085
(3) u' ^ v = ( 3, 6, 10, 13, 17, 20, 27, 34, 51, 58, 64, 71, ...) = A356086
(4) u' ^ v' = (23, 30, 37, 40, 44, 47, 54, 61, 68, 75, 78, 85, ...) = A356087
MATHEMATICA
z = 200;
r = Sqrt[2]; u = Table[Floor[n*r], {n, 1, z}] (* A001951 *)
u1 = Take[Complement[Range[1000], u], z] (* A001952 *)
r1 = Sqrt[3]; v = Table[Floor[n*r1], {n, 1, z}] (* A022838 *)
v1 = Take[Complement[Range[1000], v], z] (* A054406 *)
Intersection[u, v] (* A346308 *)
Intersection[u, v1] (* A356085 *)
Intersection[u1, v] (* A356086 *)
Intersection[u1, v1] (* A356087 *)
PROG
(Python)
from math import isqrt
from itertools import count, islice
def A356086_gen(): # generator of terms
return filter(lambda n:n == isqrt(3*(isqrt(n**2//3)+1)**2), ((k:=n<<1)+isqrt(k*n) for n in count(1)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 04 2022
STATUS
approved