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%I #31 Sep 08 2022 08:46:17
%S 3,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,
%T 3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,
%U 3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3
%N First differences of the Beatty sequence A001952 for 2 + sqrt(2).
%C Shifted by 1 (as one should) this is the unique fixed point of the morphism 3 -> 34, 4 -> 343. See A159684. - _Michel Dekking_, Aug 25 2019
%H Andrew Howroyd, <a href="/A276864/b276864.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = floor(n*r) - floor(n*r - r), where r = 2 + sqrt(2), n >= 1.
%F a(n) = 2 + floor(n*sqrt(2)) - floor((n-1)*sqrt(2)). - _Andrew Howroyd_, Feb 15 2018
%t z = 500; r = 2+Sqrt[2]; b = Table[Floor[k*r], {k, 0, z}]; (* A001952 *)
%t Differences[b] (* A276864 *)
%o (PARI) a(n) = 2 + sqrtint(2*n^2) - sqrtint(2*(n-1)^2) \\ _Andrew Howroyd_, Feb 15 2018
%o (Magma) [Floor(n*(2 + Sqrt(2))) - Floor((n-1)*(2 + Sqrt(2))): n in [1..100]]; // _G. C. Greubel_, Aug 16 2018
%Y Cf. A001952, A006337, A276882.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Sep 24 2016
%E Name corrected by _Michel Dekking_, Aug 25 2019
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