cp's OEIS Frontend

A183294 Complement of A005449.

%I A183294 #11 Nov 04 2024 22:03:08
%S A183294 1,3,4,5,6,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,27,28,29,
%T A183294 30,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,53,
%U A183294 54,55,56,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,78,79,80,81,82,83,84,85,86,87
%N A183294 Complement of A005449.
%F A183294 (See the Mathematica code.)
%F A183294 a(n) = n + A180447(n-1). - _Kevin Ryde_, Sep 01 2024
%F A183294 a(n) = n+m+1 if 2n>=m(3m+5)+4 and a(n) = n+m otherwise where m = floor(sqrt(2n/3)). - _Chai Wah Wu_, Nov 04 2024
%t A183294 a=3/2; b=1/2;
%t A183294 F[n_]:=a*n^2+b*n;
%t A183294 R[n_]:=(n/a+((b-1)/(2a))^2)^(1/2);
%t A183294 G[n_]:=n-1+Ceiling[R[n]-(b-1)/(2a)];
%t A183294 Table[F[n], {n,60}]
%t A183294 Table[G[n], {n,100}]
%o A183294 (PARI) a(n) = n + (sqrtint(24*n)+1)\6; \\ _Kevin Ryde_, Sep 01 2024
%o A183294 (Python)
%o A183294 from math import isqrt
%o A183294 def A183294(n): return n+(m:=isqrt((k:=n<<1)//3))+(k>=m*(3*m+5)+4) # _Chai Wah Wu_, Nov 04 2024
%Y A183294 Cf. A005449, A180447.
%K A183294 nonn,easy
%O A183294 1,2
%A A183294 _Clark Kimberling_, Jan 03 2011