A184118 Upper s(n)-Wythoff sequence, where s(n) = 2n + 1.

4, 7, 10, 14, 17, 21, 24, 28, 31, 34, 38, 41, 45, 48, 51, 55, 58, 62, 65, 68, 72, 75, 79, 82, 86, 89, 92, 96, 99, 103, 106, 109, 113, 116, 120, 123, 127, 130, 133, 137, 140, 144, 147, 150, 154, 157, 161, 164, 168, 171, 174, 178, 181, 185, 188, 191, 195, 198, 202, 205, 208, 212, 215, 219, 222, 226, 229, 232, 236, 239, 243, 246, 249, 253, 256, 260, 263, 267, 270, 273, 277, 280, 284, 287, 290, 294, 297, 301, 304, 307, 311, 314, 318, 321, 325, 328, 331, 335, 338, 342

Offset

1,1

Comments

See A184117 (the lower s(n)-Wythoff sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) = A184117(n) + s(n) for all n. - M. F. Hasler, Jan 07 2019

Maple

a:=n->floor((2+sqrt(2))*n+sqrt(2)/2): seq(a(n), n=1..80); # Muniru A Asiru, Jan 08 2019

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, 80}] (* Vincenzo Librandi, Jan 07 2019 *)

Prog

(PARI) A184118_upto(N, s(n)=2*n+1, U=[0], b=[])={until(b[#b]>=N, b=concat(b, s(1+#b)+U[1]+=1); U=setunion(U, [b[#b]]); while(#U>1&&U[2]==U[1]+1, U=U[^1])); b} \\ M. F. Hasler, Jan 07 2019
(Magma) [Floor((2+Sqrt(2))*n+Sqrt(2)/2): n in [1..100]]; // Vincenzo Librandi, Jan 07 2019

Crossrefs

Cf. A000201, A001950, A001950, A001951, A136119, A184117.

Sequence in context: A138813 A310689 A184625 * A310690 A310691 A161187

Adjacent sequences: A184115 A184116 A184117 * A184119 A184120 A184121

Keyword

nonn

Author

Clark Kimberling, Jan 09 2011

Status

approved