The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 0
 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 19, 24, 29, 34, 39, 44 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, ..." 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. LINKS Mehdi Hage-Hassan, An elementary introduction to Quantum mechanic, hal-00879586 2013 pp 58. EXAMPLE 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. MATHEMATICA 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; plst[n_] := Select[ulst, Ceiling[n/2]<=#

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 20 22:36 EDT 2021. Contains 343140 sequences. (Running on oeis4.)