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%I A003153 M1331 #30 Feb 17 2023 22:19:00
%S A003153 2,5,7,10,12,14,17,19,22,24,27,29,31,34,36,39,41,43,46,48,51,53,56,58,
%T A003153 60,63,65,68,70,72,75,77,80,82,84,87,89,92,94,97,99,101,104,106,109,
%U A003153 111,113,116,118,121,123,126,128,130,133,135,138,140,142,145
%N A003153 a(n) = integer nearest n*(1+sqrt(2)).
%D A003153 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003153 G. C. Greubel, <a href="/A003153/b003153.txt">Table of n, a(n) for n = 1..10000</a>
%H A003153 L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., <a href="http://www.fq.math.ca/Scanned/10-5/carlitz1.pdf">Pellian representatives</a>, Fibonacci Quarterly, 10, issue 5, 1972, 449-488.
%t A003153 ni[n_]:=Module[{c=1+Sqrt[2],a,b,x},x=c n;a=Floor[x];b=Ceiling[x]; If[x-a<b-x,a,b]]; Array[ni,60] (* _Harvey P. Dale_, May 04 2011 *)
%t A003153 Table[Round[n*(1 + Sqrt[2])], {n, 1, 100}] (* _G. C. Greubel_, Aug 16 2018 *)
%o A003153 (PARI) a(n) = round(n*(1+sqrt(2))); \\ _Michel Marcus_, Sep 07 2017
%o A003153 (Magma) [Round(n*(1+Sqrt(2))): n in [1..100]]; // _G. C. Greubel_, Aug 16 2018
%K A003153 nonn,easy
%O A003153 1,1
%A A003153 _N. J. A. Sloane_
%E A003153 Better description 1/97.

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