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

Charles Greathouse charles.greathouse at case.edu
Fri Oct 29 16:09:28 CEST 2010

```The next term for the first sequence is
9036922116709843444667289331349853231276337589593114741410804131
which I think is small enough to include.  The following terms,
12355366845323469407695932924035505500374277313036075181159979150727844474041868783907397559846490718062396654680768495555665511
and
29956212424447858025062690134791986796991384045188530821987961908306122190496805082484077678003192733750395459460647283196024172587182560740784030074216816205081616404126696536544024089426239958196186959434795214693673792511849311888613909587659101203097
are too large.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Oct 29, 2010 at 7:31 AM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
>
> 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
>
>
>
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>

```