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URL: https://oeis.org/A177732

⇱ A177732 - OEIS

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A177732
The sums of two or more consecutive positive numbers, the largest being even.
1
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
1,1
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
EXAMPLE
3=1+2, 7=3+4, 9=2+3+4, 10=1+2+3+4, 11=5+6,..
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved