# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a087278 Showing 1-1 of 1 %I A087278 #25 Sep 14 2022 02:02:10 %S A087278 0,1,2,3,4,5,8,9,10,15,16,17,24,25,26,35,36,37,48,49,50,63,64,65,80, %T A087278 81,82,99,100,101,120,121,122,143,144,145,168,169,170,195,196,197,224, %U A087278 225,226,255,256,257,288,289,290,323,324,325,360,361,362,399,400,401 %N A087278 Nonnegative integers whose distance to the nearest square is not greater than 1. %H A087278 Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1). %F A087278 a(3*k) = (k+1)^2 - 1 = A005563(k+1); %F A087278 a(3*k+1) = (k+1)^2 = A000290(k+1); %F A087278 a(3*k+2) = (k+1)^2 + 1 = A002522(k+1). %F A087278 a(n) = floor(n/3)*(floor(n/3) + 2) + n mod 3. %F A087278 G.f.: -x*(1+x)*(x^4-2*x^3+x^2+1) / ( (1+x+x^2)^2*(x-1)^3 ). - _R. J. Mathar_, May 22 2019 %F A087278 From _Amiram Eldar_, Sep 14 2022: (Start) %F A087278 Sum_{n>=1} 1/a(n) = coth(Pi)*Pi/2 + Pi^2/6 + 1/4. %F A087278 Sum_{n>=1} (-1)^(n+1)/a(n) = cosech(Pi)*Pi/2 + Pi^2/12 - 1/4. (End) %t A087278 dnsQ[n_]:=Module[{x=Floor[Sqrt[n]]},Min[n-x^2,(x+1)^2-n]<=1]; Select[Range[0,450],dnsQ] (* _Harvey P. Dale_, May 25 2011 *) %t A087278 Table[n^2+{-1,0,1},{n,20}]//Flatten (* _Harvey P. Dale_, Jan 17 2022 *) %o A087278 (Python) %o A087278 def A087278(n): %o A087278 a, b = divmod(n,3) %o A087278 return a*(a+2)+b # _Chai Wah Wu_, Aug 03 2022 %Y A087278 Union of A005563, A000290 and A002522. %Y A087278 Cf. A002264, A010872, A087279. %K A087278 nonn,easy %O A087278 0,3 %A A087278 _Reinhard Zumkeller_, Aug 28 2003 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE