

A066096


Duplicate values in A060143.


7



0, 1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 101, 103, 105, 106
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OFFSET

0,3


COMMENTS

a(n) is the smallest number different from a(i) and a(i)+i for i < n.
The losing positions in the game of WythoffNim are precisely the pairs (a(n), a(n)+n).


LINKS

Table of n, a(n) for n=0..66.


FORMULA

a(n) = 1 + A022342(n) = A000201(n).
a(n) = floor(n*phi), where phi = (1 + sqrt(5))/2.  Peter Munn, Jan 12 2018


MATHEMATICA

a[n_]:=Floor[GoldenRatio*n]; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 21 2008 *)


CROSSREFS

Cf. A000201, A003622, A022342, A035336, A060143.
Sequence in context: A064724 A285676 A085270 * A000201 A090908 A292644
Adjacent sequences: A066093 A066094 A066095 * A066097 A066098 A066099


KEYWORD

nonn,easy


AUTHOR

Michele Dondi (bik.mido(AT)tiscalenet.it), Dec 30 2001


EXTENSIONS

Name corrected by Peter Munn, Dec 06 2017


STATUS

approved



