A381189 Ulam numbers that are squarefree semiprimes.

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, 1387, 1389

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.

Number such as 4, 2809, 3481, 6889, etc., are in A378795 but not in this or in a longer sequence.

Links

Table of n, a(n) for n=1..53.

Example

4 is not a term of this sequence because 4=2^2 is the product of 2 not distinct primes even if 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.
2809 is not a term of a longer sequence because 2809=53^2 is the product of 2 not distinct primes even if 2809 is an Ulam number.

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, FactorInteger[#][[;; , 2]] == {1, 1} &]]; seq[160] (* Amiram Eldar, Feb 16 2025, after Jean-François Alcover at A002858 *)

Crossrefs

Intersection of A006881 and A002858.

Cf. A068820, A378795, A379162, A379532.

Sequence in context: A075456 A166728 A285453 * A327713 A136892 A254527

Adjacent sequences: A381186 A381187 A381188 * A381190 A381191 A381192

Keyword

nonn,new

Author

Massimo Kofler, Feb 16 2025

Status

approved