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

Jonathan Post jvospost3 at gmail.com
Thu Oct 28 20:27:22 CEST 2010

For the semiprime (A001358) analogue of
A181503 Slowest-growing sequence of primes where 1/(p+1) sums to 1
without actually reaching it.

One has:

(1/4) + (1/6) + (1/ 9) + (1/10) + (1/14) + (1/15) + (1/21) + (1/22) +
(1/25) + (1/26) + (1/33) + (1/34) = 15271237/15315300 < 1

and

(1/4) + (1/6) + (1/ 9) + (1/10) + (1/14) + (1/15) + (1/21) + (1/22) +
(1/25) + (1/26) + (1/33) + (1/34) + (1/35) = 15708817/15315300 > 1

Further steps by greedy algorithm should be simple for someone with
MAPLE or Mathematica...

Next, for 1/(1+A001358(n)):

(1/5) + (1/7) + (1/ 10) + (1/11) + (1/15) + (1/16) + (1/22) + (1/23) +
(1/26) + (1/27) + (1/34) + (1/35) + (1/36) + (1/39) + (1/40) + (1/47)
= 39139707689/39734014320  < 1

and

(1/5) + (1/7) + (1/ 10) + (1/11) + (1/15) + (1/16) + (1/22) + (1/23) +
(1/26) + (1/27) + (1/34) + (1/35) + (1/36) + (1/39) + (1/40) + (1/47)
+ (1/50) = 199671939877/198670071600  > 1

I am busy and so can't take more time right now.  But this might be made into an
OEIS seq, if it is not already...