A184414 -id:A184414 - cp's OEIS frontend

A184413 Lower s(n)-Wythoff sequence, where s(n)=floor[(n+1)/2]; complement of A184414.

1, 3, 5, 6, 9, 10, 11, 14, 16, 17, 19, 20, 23, 24, 27, 28, 29, 32, 33, 34, 37, 39, 40, 42, 45, 46, 47, 49, 51, 53, 55, 56, 57, 60, 62, 64, 65, 67, 69, 70, 73, 75, 76, 78, 79, 81, 83, 85, 87, 88, 91, 92, 93, 95, 97, 99, 101, 103, 105, 106, 108, 110, 111, 114, 115, 116, 119, 121, 123, 124, 126, 128, 129, 131, 133, 134, 137, 138, 140, 142, 144, 145, 147, 150, 151, 152, 154, 156, 157, 160, 161, 163, 165, 167, 169, 170, 173, 174, 175, 178

Offset: 1

Clark Kimberling, Jan 13 2011

nonn

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

			s=(1,1,2,2,3,3,4,4,5,5,6,6,7,7,...)=A004526;
a=(1,3,5,6,9,10,11,14,16,17,19,...)=A184413;
b=(2,4,7,8,12,13,15,18,21,22,25,...)=A184414;
Briefly: b=s+a; where a(n)=mex="least missing".

Cf. A184117, A184414.

mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
s[n_]:=Floor[(n+1)/2];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,20}]
Table[a[n],{n,100}]
Table[b[n],{n,100}]

A184410 Ranks of (odd i)+j/r when all i+j/r are ranked; r=sqrt(2), i>=0, j>=0. Complement of A184411.

Original entry on oeis.org

3, 5, 8, 11, 12, 15, 16, 20, 21, 25, 26, 27, 31, 32, 33, 38, 39, 40, 44, 46, 47, 48, 52, 54, 55, 57, 61, 63, 64, 66, 69, 71, 73, 74, 76, 79, 81, 83, 85, 87, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 119, 121, 123, 125, 127, 129

Offset: 1

Clark Kimberling, Jan 13 2011

nonn

			Writing (i,j) for i+j/r, the first 7 in the ranking are (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), (0,3); the ranks where i is odd are 3,5 and the ranks where i is even are 1,2,4,6,7.

Cf. A184397, A184411, A184412, A184413, A184414, A184415, A184416.

A184411 Ranks of (even i)+j/r when all i+j/r are ranked; r=sqrt(2), i>=0, j>=0. Complement of A184410.

Original entry on oeis.org

1, 2, 4, 6, 7, 9, 10, 13, 14, 17, 18, 19, 22, 23, 24, 28, 29, 30, 34, 35, 36, 37, 41, 42, 43, 45, 49, 50, 51, 53, 56, 58, 59, 60, 62, 65, 67, 68, 70, 72, 75, 77, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 118, 120

Offset: 1

Clark Kimberling, Jan 13 2011

nonn

			Writing (i,j) for i+j/r, the first 7 in the ranking are (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), (0,3); the ranks where i is odd are 3,5 and the ranks where i is even are 1,2,4,6,7.

Cf. A184397, A184410, A184412, A184413, A184414, A184415, A184416.

cp's OEIS Frontend

A184413 Lower s(n)-Wythoff sequence, where s(n)=floor[(n+1)/2]; complement of A184414.

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A184410 Ranks of (odd i)+j/r when all i+j/r are ranked; r=sqrt(2), i>=0, j>=0. Complement of A184411.

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A184411 Ranks of (even i)+j/r when all i+j/r are ranked; r=sqrt(2), i>=0, j>=0. Complement of A184410.

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