A379162 Ulam numbers that are sphenics.

102, 114, 138, 182, 238, 258, 273, 282, 370, 402, 429, 434, 483, 602, 627, 646, 861, 986, 1023, 1030, 1311, 1335, 1338, 1406, 1462, 1790, 1834, 1902, 1946, 2054, 2093, 2134, 2247, 2330, 2354, 2445, 2486, 2613, 2630, 2635, 2674, 2919, 2985, 3070, 3219, 3395

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

102 is a term because 102=2*3*17 is the product of 3 distinct primes and 102 is an Ulam number.
114 is a term because 114=2*3*19 is the product of 3 distinct primes and 114 is an Ulam number.
273 is a term because 273=3*7*13 is the product of 3 distinct primes and 273 is an Ulam number.

Maple

N:= 10^4: # for terms <= N
U:= [1, 2]: V:= Vector(N): V[3]:= 1: R:= NULL:
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];
       F:= ifactors(k)[2]:
       if F[.., 2] = [1, 1, 1] then R:= R, k; break fi
   od;
   if k > N then break fi;
od:
R; # Robert Israel, Jan 03 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, FactorInteger[#][[;; , 2]] == {1, 1, 1} &]]; seq[300] (* Amiram Eldar, Dec 17 2024, after Jean-François Alcover at A002858 *)

Crossrefs

Intersection of A002858 and A007304.

Cf. A068820, A378795.

Sequence in context: A127665 A097037 A035480 * A181986 A107838 A095637

Adjacent sequences: A379159 A379160 A379161 * A379163 A379164 A379165

Keyword

nonn

Author

Massimo Kofler, Dec 17 2024

Status

approved