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A184922 n+[rn/t]+[sn/t]+[un/t], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3. 7
2, 5, 9, 12, 16, 19, 22, 26, 29, 33, 36, 39, 43, 46, 50, 53, 57, 60, 63, 67, 70, 74, 77, 80, 84, 87, 91, 94, 98, 101, 104, 108, 111, 115, 118, 121, 125, 128, 132, 135, 138, 142, 145, 149, 152, 156, 159, 162, 166, 169, 173, 176, 179, 183, 186, 190, 193, 197, 200, 203, 207, 210, 214, 217, 220, 224, 227, 231, 234, 237, 241, 244, 248, 251, 255, 258, 261, 265, 268, 272, 275, 278, 282, 285, 289, 292, 296, 299, 302, 306, 309, 313, 316, 319, 323, 326, 330, 333, 337, 340, 343, 347, 350, 354, 357, 360, 364, 367, 371, 374, 377, 381, 384, 388, 391, 395, 398, 401, 405, 408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Since [rn/t]=sqrt(2)-1, [sn/t]=sqrt(2)/2, and [un/t]=2-sqrt(2)/2, we find using [-x]=-[x]-1 for non-integer x, that a(n)= floor(n*(2+sqrt(2)))-1 = A001952(n)-1. - Michel Dekking, Feb 22 2018

LINKS

Table of n, a(n) for n=1..120.

FORMULA

a(n) = floor(n*(2+sqrt(2)))-1. - Michel Dekking, Feb 22 2018

MATHEMATICA

The sequences A184920-A184923 partition the positive integers:

  A184920: 7, 15, 24, 31, 40, 48, 55, 64, ...

  A184921: 3, 8, 13, 18, 23, 27, 32, 37, ...

  A184922: 2, 5, 9, 12, 16, 19, 22, 26, 29, ...

  A184923: 1, 4, 6, 10, 11, 14, 17, 20, 21, ...

Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},

where h>=1, i>=1, j>=1, k>=1.  The position of n*t in the joint ranking is n+[rn/t]+[sn/t]+[un/t], and likewise for the positions of n*s, n*s, and n*u.

CROSSREFS

Cf. A184912, A184921, A184921, A184923, A001952.

Sequence in context: A184926 A342745 A189384 * A189461 A190506 A047385

Adjacent sequences:  A184919 A184920 A184921 * A184923 A184924 A184925

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 26 2011

EXTENSIONS

Name corrected by Michel Dekking, Feb 22 2018

STATUS

approved

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Last modified August 7 22:13 EDT 2022. Contains 355995 sequences. (Running on oeis4.)