A378795 Ulam numbers that are semiprimes.

4, 6, 26, 38, 57, 62, 69, 77, 82, 87, 106, 145, 155, 177, 206, 209, 219, 221, 253, 309, 319, 339, 341, 358, 382, 451, 485, 497, 502, 566, 685, 695, 734, 781, 849, 866, 893, 905, 949, 1018, 1037, 1079, 1081, 1101, 1157, 1167, 1169, 1186, 1191, 1257, 1313, 1355

Offset

1,1

Comments

Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

4 is a term because 4=2*2 is the product of 2 (not distinct) primes and 4 is an Ulam number.
6 is a term because 6=2*3 is the product of 2 distinct primes and 6 is an Ulam number.
57 is a term because 57=3*19 is the product of 2 distinct primes and 57 is an Ulam number.

Maple

N:= 5000: # for terms <= N
U:= [1, 2]: V:= Vector(N): V[3]:= 1: R:= NULL: count:= 0:
for i from 3 do
   for k from U[-1]+1 to N do
     if V[k] = 1 then
       J:= select(`<=`, U +~ k, N);
       V[J]:= V[J] +~ 1;
       U:= [op(U), k];
       if numtheory:-bigomega(k) = 2 then R:= R, k; count:= count+1;  fi;
       break
     fi
   od;
   if k > N then break fi;
od:
R; # Robert Israel, Jan 24 2025

Mathematica

seq[numUlams_] := Module[{ulams = {1, 2}}, Do[AppendTo[ulams, n = Last[ulams]; While[n++; Length[DeleteCases[Intersection[ulams, n - ulams], n/2, 1, 1]] != 2]; n], {numUlams}]; Select[ulams, PrimeOmega[#] == 2 &]]; seq[200] (* Amiram Eldar, Dec 07 2024, after Jean-François Alcover at A002858 *)

Crossrefs

Intersection of A001358 and A002858.

Cf. A068820.

Sequence in context: A028273 A024471 A075277 * A370061 A192874 A371869

Adjacent sequences: A378792 A378793 A378794 * A378796 A378797 A378798

Keyword

nonn

Author

Massimo Kofler, Dec 07 2024

Status

approved