A033629 Numbers that are not the sum of two distinct Ulam numbers.

23, 25, 33, 35, 43, 45, 67, 92, 94, 96, 111, 121, 136, 143, 160, 165, 170, 172, 187, 194, 204, 226, 231, 248, 265, 270, 280, 287, 292, 297, 302, 304, 314, 331, 336, 346, 348, 353, 368, 380, 397, 407, 419, 424, 446, 463, 468, 473, 475, 480, 490, 495, 507

Offset: 1

Author

Jud McCranie

Keywords

• nonn

References

• R. K. Guy, Unsolved Problems in Number Theory, C4

Links

• Ruud H.G. van Tol, Table of n, a(n) for n = 1..11944 (upto 2^16)
• Shyam Sunder Gupta, Ulam Numbers. In: Exploring the Beauty of Fascinating Numbers. Springer Praxis Books(). Springer, Singapore, (2025).
• Ivano Salvo and Agnese Pacifico, Computing Integer Sequences: Filtering vs Generation (Functional Pearl), arXiv:1807.11792 [cs.PL], 2018.

Crossrefs

Cf. A002858.

Programs

Mathematica

terms = 1000; ulams = {1, 2};
Do[AppendTo[ulams, n = Last[ulams]; While[n++; Length[ DeleteCases[ Intersection[ ulams, n - ulams], n/2, 1, 1]] != 2]; n], {terms}];
uu = Total /@ Subsets[ulams, {2}] // Union;
Complement[Range[Last[uu]], uu] // Take[#, {3, terms+2}]& (* Jean-François Alcover, Dec 02 2018 *)

PARI

aupto(N)= my(S=Vec([1, 1], N), U=[]); for(i=1, N, if(1==S[i], for(j=1, #U, my(t=i+U[j]); if(t>N, break); S[t]++); U=concat(U, i))); Vec(select(x->!x, S, 1)) \\ Ruud H.G. van Tol, Jul 05 2025