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 A356086 Intersection of A001952 and A022838. 4
 3, 6, 10, 13, 17, 20, 27, 34, 51, 58, 64, 71, 81, 88, 95, 102, 105, 109, 112, 116, 119, 122, 126, 129, 133, 136, 143, 150, 157, 174, 180, 187, 204, 211, 218, 221, 225, 228, 232, 235, 242, 245, 249, 252, 256, 259, 266, 273, 284, 285, 287, 289, 290, 292, 294 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Table of n, a(n) for n=1..55. 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))) A356086_list = list(islice(A356086_gen(), 30)) # Chai Wah Wu, Aug 06 2022 CROSSREFS Cf. A001951, A001952, A022838, A054406, A346308, A356085, A356087, A356088 (results of composition instead of intersections). Sequence in context: A047280 A310054 A310055 * A310056 A189524 A288205 Adjacent sequences: A356083 A356084 A356085 * A356087 A356088 A356089 KEYWORD nonn,easy AUTHOR Clark Kimberling, Aug 04 2022 STATUS approved

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Last modified August 14 10:24 EDT 2024. Contains 375159 sequences. (Running on oeis4.)