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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A002858.

Sequence in context: A054795 A305469 A093805 * A090311 A172015 A112073

Adjacent sequences: A033626 A033627 A033628 * A033630 A033631 A033632

Keyword

nonn

Author

Jud McCranie

Status

approved