This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A322605 #15 Jul 12 2023 11:08:01
%S A322605 2,3,4,5,6,7,8,9,10,12,14,17,19,24,29,34,39,44
%N A322605 Numbers k such that all k - u are Ulam numbers (A002858) where u is an Ulam number in the range k/2 <= u < k.
%C A322605 The following is a quotation from Hage-Hassan in his paper (see Link below). "The (concept of) right and left symmetry is fundamental in physics. This incites us to ask whether this symmetry is in (the) primes. Find the numbers n with a + a' = n. a, a' are primes and {a} are all the primes with: n/2 <= a < n and n = 2,3, ..."
%C A322605 This sequence is analogous to A320447. Instead of the sequence of primes it uses the sequence of Ulam numbers (A002858). It is conjectured that the sequence is finite and full.
%H A322605 Mehdi Hage-Hassan, <a href="https://hal.archives-ouvertes.fr/hal-00879586/document">An elementary introduction to Quantum mechanic</a>, hal-00879586 2013 pp 58.
%e A322605 a(10)=12, because the Ulam numbers u in the range 6 <= u < 12 are {6, 8, 11}. Also the complementary set {6, 4, 1} has all its members Ulam numbers. This is the 10th occurrence of such a number.
%t A322605 Ulam[n_] := Module[{ulams={1, 2}, p}, Do[AppendTo[ulams, p=Last[ulams]; While[p++; Length[DeleteCases[Intersection[ulams, p-ulams], p/2, 1, 1]]!=2]; p], {n-2}]; ulams]; ulst=Ulam[1000]; plst[n_] := Select[ulst, Ceiling[n/2]<=#<n &]; lst={}; Do[If[plst[n]!={}&&Intersection[ulst, nlst=Sort[n-plst[n]]]==nlst, AppendTo[lst, n]], {n, 1, 1000}]; lst
%Y A322605 Cf. A002858, A320447.
%K A322605 nonn,more
%O A322605 1,1
%A A322605 _Frank M Jackson_, Dec 20 2018