A051611 Numbers that are not the sum of 2 nonzero triangular numbers.

1, 3, 5, 8, 10, 14, 15, 17, 19, 23, 26, 28, 32, 33, 35, 40, 41, 44, 45, 47, 50, 52, 53, 54, 59, 62, 63, 68, 71, 74, 75, 77, 78, 80, 82, 85, 86, 89, 95, 96, 98, 103, 104, 105, 107, 109, 113, 116, 117, 118, 122, 124, 125, 128, 129, 131, 134, 138, 140, 143, 145, 147

Offset: 1

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)

Keywords

• easy
• nonn
• nice

Comments

A053603(a(n)) = 0. - Reinhard Zumkeller, Jun 28 2013

Links

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

Crossrefs

Integers not in the sequence A051533. Cf. A002097, A000217, A007294, A051611, A053603.

Programs

Haskell

a051611 n = a051611_list !! (n-1)
a051611_list = filter ((== 0) . a053603) [1..]
-- Reinhard Zumkeller, Jun 28 2013

Mathematica

notSumQ[n_] := Reduce[ 0 < x <= y && n == x*(x + 1)/2 + y*(y + 1)/2, {x, y}, Integers] === False; Select[ Range[150], notSumQ] (* Jean-François Alcover, Jun 27 2012 *)
With[{trnos=Accumulate[Range[100]]},Complement[Range[150],Total/@ Tuples[ trnos,2]]] (* Harvey P. Dale, Jun 01 2016 *)