[seqfan] Re: semiprime (A001358) analogue of A181503 Slowest-growing sequence of primes where 1/(p+1) sums to 1...

[Richard Mathar]

More terms on behalf of http://list.seqfan.eu/pipermail/seqfan/2010-October/006328.html
(not submitted):


%I A000001
%S A000001 4,6,9,10,14,15,21,22,25,26,33,34,355,16627,76723511,17218740226618333,
%T A000001 374886275842473712491638217368219
%N A000001 Smallest growing sequence of semiprimes A001358 such that sum_{i=1..n} 1/a(i) < 1 for all n.
%C A000001 Semiprime variant of A075442.
%C A000001 The first semiprime that is not in the sequence is 35, because 1/4+1/6+1/9+..+1/34+1/35 > 1.
%p A000001 A := proc(n) option remember; local a,psum; if n = 1 then A001358(1); else psum := add(1/procname(i),i=1..n-1) ;
                for a from max(procname(n-1)+1,ceil(1/(1-psum)) ) do if isA001358(a) then if psum+1/a < 1 then
                return a; end if; end if; end do: end if; end proc: # R. J. Mathar, Oct 29 2010 
%K A000001 nonn,new
%O A000001 1,1
%A A000001 Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 29 2010


%I A000002
%S A000002 5,7,10,11,15,16,22,23,26,27,34,35,36,39,40,47,70,1498,259466,4852747704,
%T A000002 27172017624687178982,72672016993293266604838074954037471958
%N A000002 Smallest growing sequence of incremented semiprimes A088707 such that sum_{i=1..n} 1/a(i) < 1 for all n.
%C A000002 Semiprime variant of A181503.
%e A000002 1/(4+1)+1/(6+1)+1/(9+1)+1/(10+1)+1/(14+1)+... <1.
%p A000002 isA088707 := proc(n) numtheory[bigomega](n-1) = 2 ; end:
%p A000002 A088707 := proc(n) option remember; local a; if n = 1 then 5; else for a from procname(n-1)+1 do
                        if isA001358(a-1) then return a; end if; end do: end if; end proc:
%p A000002 A := proc(n) option remember; local a,psum; if n = 1 then A088707(1); else
                psum := add(1/procname(i),i=1..n-1) ; for a from max(procname(n-1)+1,ceil(1/(1-psum)) ) do
                if isA088707(a) then if psum+1/a < 1 then return a; end if; end if;
                end do: end if; end proc: # R. J. Mathar, Oct 29 2010
%K A000002 nonn,new
%O A000002 1,1
%A A000002 Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 29 2010