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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
Programs
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Magma
[Floor((2+Sqrt(2))*n+Sqrt(2)/2): n in [1..100]]; // Vincenzo Librandi, Jan 07 2019
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Maple
a:=n->floor((2+sqrt(2))*n+sqrt(2)/2): seq(a(n),n=1..80); # Muniru A Asiru, Jan 08 2019
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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 *) -
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
Formula
a(n) = A184117(n) + s(n) for all n. - M. F. Hasler, Jan 07 2019
Comments