

A184419


Lower sWythoff sequence, where s=lower Wythoff sequence. Complement of A184420.


3



1, 3, 4, 5, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 79, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 108, 109, 110, 112, 114, 115, 116, 118, 119, 121, 122, 124, 125, 127, 128, 130, 131, 133, 134, 135, 137, 139, 140, 141, 143, 144, 146, 148
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..100.


EXAMPLE

s=(1,3,4,6,8,9,11,12,...)=A000201=lower Wythoff sequence;
a=(1,3,4,5,7,9,10,12,...)=A184419;
b=(2,6,8,11,15,18,21,24,...)=A184420.
Briefly: b=s+a, where a=mex="least missing".


MATHEMATICA

mex:=First[Complement[Range[1, Max[#1]+1], #1]]&;
r=(1+5^(1/2))/2; s[n_]:=Floor[r*n]; a[1]=1; b[n_]:=b[n]=s[n]+a[n];
a[n_]:=a[n]=mex[Flatten[Table[{a[i], b[i]}, {i, 1, n1}]]];
Table[s[n], {n, 40}]
Table[a[n], {n, 100}]
Table[b[n], {n, 100}]


CROSSREFS

Cf. A184117, A000201, A184420.
Sequence in context: A183213 A183172 A136495 * A285970 A189665 A156246
Adjacent sequences: A184416 A184417 A184418 * A184420 A184421 A184422


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jan 13 2011


STATUS

approved



