[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...
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