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A184419 Lower s-Wythoff 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 (list; graph; refs; listen; history; text; internal format)
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, n-1}]]];

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

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Last modified November 26 13:21 EST 2022. Contains 358362 sequences. (Running on oeis4.)