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A137803 a(n) = floor(n*(sqrt(2) + 1/2)).

%I A137803 #21 Feb 16 2025 08:33:07
%S A137803 1,3,5,7,9,11,13,15,17,19,21,22,24,26,28,30,32,34,36,38,40,42,44,45,
%T A137803 47,49,51,53,55,57,59,61,63,65,66,68,70,72,74,76,78,80,82,84,86,88,89,
%U A137803 91,93,95,97,99,101,103,105,107,109,111,112,114,116,118,120,122,124,126
%N A137803 a(n) = floor(n*(sqrt(2) + 1/2)).
%C A137803 a(n) = A059533(n) for n <= 34;
%C A137803 Beatty sequence for sqrt(2) + 1/2; complement of A137804;
%C A137803 a(n) = A137805(A137804(n)) and A137805(a(n)) = A137804(n).
%H A137803 G. C. Greubel, <a href="/A137803/b137803.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from R. Zumkeller)
%H A137803 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>
%H A137803 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%t A137803 Floor[Range[80](Sqrt[2]+1/2)]  (* _Harvey P. Dale_, Mar 24 2011 *)
%o A137803 (PARI) for(n=1,50, print1(floor(n*(sqrt(2)+1/2)), ", ")) \\ _G. C. Greubel_, Jan 27 2018
%o A137803 (Magma) [Floor(n*(Sqrt(2)+1/2)): n in [1..50]]; // _G. C. Greubel_, Jan 27 2018
%o A137803 (Python)
%o A137803 from math import isqrt
%o A137803 def A137803(n): return (n>>1)+(m:=isqrt(r:=n*n<<1))+(n&1)*int(r-m*(m+1)>=1) # _Chai Wah Wu_, Aug 03 2022
%Y A137803 Cf. A001951, A003151.
%K A137803 nonn
%O A137803 1,2
%A A137803 _Reinhard Zumkeller_, Feb 11 2008