A119345 Numbers having exactly one representation as sum of two triangular numbers.

0, 1, 2, 3, 4, 7, 9, 10, 11, 12, 13, 15, 18, 20, 22, 24, 25, 27, 28, 29, 30, 34, 37, 38, 39, 43, 45, 48, 49, 57, 58, 60, 61, 64, 65, 67, 69, 70, 73, 78, 79, 83, 84, 87, 88, 90, 92, 93, 97, 99, 100, 101, 102, 105, 108, 110, 112, 114, 115, 119, 127, 130, 132, 135, 137, 139, 142

Offset: 1

Author

Reinhard Zumkeller, May 15 2006

Keywords

• nonn

Comments

A052343(a(n)) = 1; gives A020756 together with A118139.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020757, A000217.

Cf. A020756, A052343, A118139.

Programs

Haskell

a119345 n = a119345_list !! (n-1)
a119345_list = filter ((== 1) . a052343) [0..]
-- Reinhard Zumkeller, Jul 25 2014

Mathematica

trn=SortBy[{First[#],Last[#],Total[#]}& /@ (Union[Sort/@Tuples[Accumulate[Range[0,70]],{2}]]),Last]; Take[With[{x=Transpose[trn][[3]]}, Complement[Union[x], Union[Flatten[Select[Split[x], Length[#]>1&]]]]],70]  (* Harvey P. Dale, Feb 14 2011 *)
nn=100; tri=Table[n(n+1)/2,{n,0,nn}]; sums=Select[Flatten[Table[tri[[i]]+tri[[j]], {i,nn}, {j,i}]], #