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 A182656 Floor-sum sequence of r, with r=sqrt(3), and a(1)=1, a(2)=2. 3

%I

%S 1,2,5,10,12,19,20,22,24,25,29,34,36,38,39,41,43,45,46,50,51,53,55,58,

%T 60,62,64,65,67,69,71,72,74,76,77,79,81,83,84,86,88,90,91,93,95,96,98,

%U 100,102,103,105,107,109,110,112,114,116,117

%N Floor-sum sequence of r, with r=sqrt(3), and a(1)=1, a(2)=2.

%C Let S be the set generated by these rules: (1) if m and n are in S and m<n, then floor(mr+nr) is in S; (2) two or more specific numbers are in S. The floor-sum sequence determined by (1) and (2) results by arranging the elements of S in strictly increasing order.

%C Let B be the Beatty sequence of r. Then a floor-sum sequence of r is a subsequence of B if and only if a(1) and a(2) are terms of B.

%e a(3)=floor(r+2r)=5.

%Y Cf. A182653, A182654, A182655, A022838.

%K nonn

%O 1,2

%A _Clark Kimberling_, Nov 26 2010

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Last modified September 25 15:27 EDT 2021. Contains 347658 sequences. (Running on oeis4.)