|
COMMENT
|
It is interesting that the number 2 occurs deep into the sequence indicating a twin prime pair. It is reasonable to ask if this will ever occur again. Similarly, the analogous sequence A074383, "Difference between (1+10^n)-th and (10^n)-th primes" has 2 occurring shallow into the sequence. It is reasonable to ask if the number 2 will ever occur again in that sequence. The link provides an excellent algorithm, primex(n), that I developed to find the n-th prime using Gram's approximation of Riemann's approximation R(x) for Pi(x). Primex(n) will give about n/2 exact digits for prime(n). For A006988 (18), primex(18) is 44211790234127235469.62904554...This is only as good as R (x) but nevertheless is superior to the exact formulas out there from a practical stand point. If we apply the code gpx(n) = for(x=1,n,y=nextprime(primex(10^x))-nextprime (primex(10^x-1));print1(floor(y)",")), we will get the eratic concoction 2,0,8,14,22,28,26,0,72,18,22,0,0,0,0,0,32,0,80,78,60,0 as an analytical counterpart of the sequence given.
|
