|
%I M1331 #30 Feb 17 2023 22:19:00
%S 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 60,63,65,68,70,72,75,77,80,82,84,87,89,92,94,97,99,101,104,106,109,
%U 111,113,116,118,121,123,126,128,130,133,135,138,140,142,145
%N a(n) = integer nearest n*(1+sqrt(2)).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. C. Greubel, <a href="/A003153/b003153.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 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 Table[Round[n*(1 + Sqrt[2])], {n, 1, 100}] (* _G. C. Greubel_, Aug 16 2018 *)
%o (PARI) a(n) = round(n*(1+sqrt(2))); \\ _Michel Marcus_, Sep 07 2017
%o (Magma) [Round(n*(1+Sqrt(2))): n in [1..100]]; // _G. C. Greubel_, Aug 16 2018
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E Better description 1/97.
|
