A177732 The sums of two or more consecutive positive numbers, the largest being even.

3, 7, 9, 10, 11, 15, 18, 19, 20, 21, 23, 26, 27, 30, 31, 33, 34, 35, 36, 39, 40, 42, 43, 45, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 63, 66, 67, 68, 69, 70, 71, 72, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 87, 90, 91, 93, 95, 98, 99, 100, 102, 103, 104, 105, 106, 107, 108

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 12 2010

Keywords

• nonn

Comments

Numbers of the form (j+2l)*(2l-j+1)/2 with j>=1 and 2l>j. Subsequences are A014105 where >=3, (j=1), A014107 where >=9 (j=2). - R. J. Mathar, Jul 14 2012

Examples

			3=1+2, 7=3+4, 9=2+3+4, 10=1+2+3+4, 11=5+6,..
		

Crossrefs

Cf. A177712, A177713, A177731.

Programs

Mathematica

z=200;lst2={};Do[c=a;Do[c+=b;If[c<=2*z,AppendTo[lst2,c]],{b,a-1,1,-1}],{a,2,z,2}];Union@lst2
With[{upto=108},Select[Union[Flatten[Table[Accumulate[Range[2n-1,1,-1]]+ 2n,{n,upto/4}]]],#<=upto&]] (* Harvey P. Dale, May 19 2019 *)