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A183218 Complement of the hexagonal numbers. 3

%I #9 Sep 22 2020 20:09:20

%S 2,3,4,5,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,29,

%T 30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,46,47,48,49,50,51,52,53,

%U 54,55,56,57,58,59,60,61,62,63,64,65,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107

%N Complement of the hexagonal numbers.

%H Harvey P. Dale, <a href="/A183218/b183218.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)=n+Floor[1/2+(n/2)^(1/2)].

%e Hexagonal numbers: (1,6,15,28,45,...) = A000384,

%e so that A183218=(2,3,4,5,7,8,9,...,14,16,...,27,29,...).

%t Table[n+Floor[1/2+(n/2)^(1/2)], {n,100}]

%t Module[{nn=110},Complement[Range[nn],PolygonalNumber[6,Range[ Floor[ (1+Sqrt[ 1+8nn])/4]]]]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 22 2020 *)

%Y Cf. A000384.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 01 2011

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