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A184413
Lower s(n)-Wythoff sequence, where s(n)=floor[(n+1)/2]; complement of A184414.
5
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
1,2
COMMENTS
See A184117 for the definition of lower and upper s(n)-Wythoff sequences.
EXAMPLE
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".
MATHEMATICA
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}]
CROSSREFS
Sequence in context: A087757 A188163 A088359 * A187345 A179185 A270198
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 13 2011
STATUS
approved