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First differences of the Beatty sequence A003231 for 2 + tau, where tau = golden ratio = (1 + sqrt(5))/2.
3

%I #9 Sep 26 2016 21:37:52

%S 3,4,3,4,4,3,4,3,4,4,3,4,4,3,4,3,4,4,3,4,3,4,4,3,4,4,3,4,3,4,4,3,4,4,

%T 3,4,3,4,4,3,4,3,4,4,3,4,4,3,4,3,4,4,3,4,3,4,4,3,4,4,3,4,3,4,4,3,4,4,

%U 3,4,3,4,4,3,4,3,4,4,3,4,4,3,4,3,4,4

%N First differences of the Beatty sequence A003231 for 2 + tau, where tau = golden ratio = (1 + sqrt(5))/2.

%H Clark Kimberling, <a href="/A276867/b276867.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(n*r) - floor(n*r - r), where r = 2 + tau, n >= 1.

%t z = 500; r = 2+GoldenRatio; b = Table[Floor[k*r], {k, 0, z}]; (* A003231 *)

%t Differences[b] (* A276867 *)

%Y Cf. A003231, A276886.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Sep 24 2016