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

1,3

Comments

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

Links

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

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}]], #<tri[[-1]]&]; Sort[First/@Select[Tally[sums], #[[2]]==1&]]

Prog

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

Crossrefs

Cf. A020757, A000217.

Cf. A020756, A052343, A118139.

Sequence in context: A182802 A172024 A285500 * A086391 A120127 A047548

Adjacent sequences: A119342 A119343 A119344 * A119346 A119347 A119348

Keyword

nonn

Author

Reinhard Zumkeller, May 15 2006

Status

approved