A181620 Sequence starting with 2 such that the sum of any two distinct terms is a semiprime having two distinct prime factors.

2, 4, 31, 91, 183, 4411, 29611, 59935, 110791, 10418851, 658653031, 20123369491, 518294316451, 947137685251

Offset: 1

Author

Michel Lagneau, Jan 31 2011

Keywords

• nonn
• more

Comments

Choose the first number not leading to a contradiction.

The sequence starting with 1 is finite: {1, 5, 9, 86, 212};

Sequence starting with 3: {3, 7, 19, 32, 55, 246, 39499, ...};

Sequence starting with 4: {4, 6, 29, 89, 137, 749, 1685, 16497, ...}.

Examples

			The subset {2, 4, 31} produces the three sums {6, 33, 35} which factor as {2*3, 3*11, 5*7}.
		

Crossrefs

Cf. A180514, A180565, A180615.

Programs

Maple

with(numtheory):nn:=500000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
  nn do: T[p]:=p+1:U[p]:=2:od:for u from 1 to 10 do: k:=1+u:for n from u+1 to
  nn do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=2 and s2=2 then
  U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
  1 to 30 do:print( T[j]):od:

Mathematica

TwoDistinct[n_]:=Module[{p,e}, {p,e}=Transpose[FactorInteger[n]]; Length[p]==2 && e=={1,1}]; t={2}; k=2; Do[While[k++; !And@@TwoDistinct/@(k+t)]; AppendTo[t,k], {6}]; t

Extensions

Removed 84835 and a(10)-a(12) from Donovan Johnson, Feb 14 2011

a(13)-a(14) from Jinyuan Wang, May 29 2025