%I #18 Apr 03 2024 15:15:34
%S 1,2,4,11,25,64,171,569,3406,27697,243374,1759619,28381401,222323189,
%T 3416307938,26838745347
%N Numbers needed to generate all other natural numbers, only allowing multiplication and addition. Each number can be used only once.
%F a(n) >= 2a(n-1). - _Charles R Greathouse IV_, Jun 17 2013
%e 10 is not in the sequence because (4+1)*2 = 10.
%e 11 is in the sequence because there is no way to get 11 by using the earlier terms.
%e 509 is not in the sequence because 509 = (1+25)*(2+11)+171.
%o (PARI) Ww(v)=if(#v==2,return([v[1],v[2],v[1]+v[2],v[1]*v[2]]));my(V=[],t);for(i=1,#v-1,for(j=i+1,#v,t=vecextract(v,2^#v-1-2^(i-1)-2^(j-1)); V=concat(V, concat(Ww(concat(t,v[i]+v[j])), Ww(concat(t,v[i]*v[j]))))); V=vecsort(V,,8));V
%o a=[1,2,4]; for(n=3,9,V=Ww(a);for(i=2*a[#a],#V,if(V[i]>i, print(a=concat(a,i));break))) \\ _Charles R Greathouse IV_, Jun 17 2013
%K more,nonn,nice
%O 1,2
%A Arno Bouwes (acbouwes(AT)hotmail.com), Sep 08 2003
%E Corrected and extended by _Don Reble_, Sep 21 2003
%E Two more terms from _Jon E. Schoenfield_, Aug 24 2009
%E a(13)-a(15) from _Giovanni Resta_, Jun 22 2013
%E a(16) from _Bert Dobbelaere_, Apr 03 2024