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A184119 Upper s(n)-Wythoff sequence, where s(n) = 2n - 1; complement of A136119. 5
2, 6, 9, 12, 16, 19, 23, 26, 30, 33, 36, 40, 43, 47, 50, 53, 57, 60, 64, 67, 70, 74, 77, 81, 84, 88, 91, 94, 98, 101, 105, 108, 111, 115, 118, 122, 125, 129, 132, 135, 139, 142, 146, 149, 152, 156, 159, 163, 166, 170, 173, 176, 180, 183, 187, 190, 193, 197, 200, 204, 207, 210, 214, 217, 221, 224, 228, 231, 234, 238, 241, 245, 248, 251, 255, 258, 262, 265, 269, 272, 275, 279, 282, 286, 289, 292, 296, 299, 303, 306, 309, 313, 316, 320, 323, 327, 330, 333, 337, 340 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A184117 for the definition of lower and upper s(n)-Wythoff sequences.

(a(n)) is an inhomogeneous Beatty sequence, the complement of the inhomogeneous Beatty sequence (A136119(n)) = (floor(sqrt(2)*n + 1 - sqrt(2)/2)). See the paper by Fraenkel. - Michel Dekking, Jan 31 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Aviezri S. Fraenkel, Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups, Transactions of the American Mathematical Society 341.2 (1994): p. 640.

FORMULA

a(n) = floor((2+sqrt(2))*n - sqrt(2)/2). - Michel Dekking, Jan 31 2017

MATHEMATICA

k=2; r=1;

mex:=First[Complement[Range[1, Max[#1]+1], #1]]&;

s[n_]:=k*n-r; a[1]=1; b[n_]:=b[n]=s[n]+a[n];

a[n_]:=a[n]=mex[Flatten[Table[{a[i], b[i]}, {i, 1, n-1}]]];

Table[s[n], {n, 30}]

Table[a[n], {n, 100}]

Table[b[n], {n, 100}]

Table[(Floor[(2 + Sqrt[2]) n - Sqrt[2]/2]), {n, 100}] (* Vincenzo Librandi, Jan 31 2017 *)

PROG

(Magma) [Floor((2+Sqrt(2))*n-Sqrt(2)/2): n in [1..80]]; // Vincenzo Librandi, Jan 31 2017

CROSSREFS

Cf. A136119, A184117.

Sequence in context: A186500 A190777 A184619 * A191873 A293789 A112870

Adjacent sequences:  A184116 A184117 A184118 * A184120 A184121 A184122

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 09 2011

STATUS

approved

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Last modified October 5 20:00 EDT 2022. Contains 357261 sequences. (Running on oeis4.)