A119345 - OEIS

%I #13 Aug 05 2014 15:37:20

%S 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,

%T 43,45,48,49,57,58,60,61,64,65,67,69,70,73,78,79,83,84,87,88,90,92,93,

%U 97,99,100,101,102,105,108,110,112,114,115,119,127,130,132,135,137,139,142

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

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

%H T. D. Noe, <a href="/A119345/b119345.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 *)

%t 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&]]

%o (Haskell)

%o a119345 n = a119345_list !! (n-1)

%o a119345_list = filter ((== 1) . a052343) [0..]

%o -- _Reinhard Zumkeller_, Jul 25 2014

%Y Cf. A020757, A000217.

%Y Cf. A020756, A052343, A118139.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, May 15 2006