%I A143935
%S A143935 2,1,2,1,2,2,2,2,2,2,3,2,2,5,1,4,2,3,3,4,1,5,3,3,4,3,3,3,4,4,3,5,4,3,5,
%T A143935 2,4,5,4,5,5,3,5,5,2,6,5,4,4,4,5,5,7,5,5,3,5,6,3,8,3,4,5,6,7,5,6,8,5,4,
%U A143935 6,6,3,7,5,4,8,5,8,6,3,7,7,6,8,7,4,5,6,5,9,9,7,6,6,6,6,7,6,4,8,5,8,8,4
%N A143935 Number of primes between n^K and (n+1)^K, inclusive, where K=1.74717117169304146332.
%C A143935 This value of K is conjectured to be the least possible such that there 
               is at least one prime in the range n^k and (n+1)^k for all n>0 and 
               k>=K. This value of K was found using exact interval arithmetic. 
               For each n <= 300 and for each prime p in the range n to n^2, we 
               computed an interval k(n,p) such that p is between n^k(n,p) and (n+1)^k(n,
               p). The intersection of all these intervals produces a list of 29 
               intervals. The last interval appears to be semi-infinite beginning 
               with K, which is log(127)/log(16). See A143898 for the smallest number 
               in the first interval.
%C A143935 My UBASIC program indicates no prime between 113.457 ... and 126.999 
               .... Next prime > 113 is 127. I would like someone to check this. 
               [From Enoch Haga (Enokh(AT)comcast.net), Sep 24 2008]
%H A143935 T. D. Noe, <a href="b143935.txt">Table of n, a(n) for n=1..10000</a>
%t A143935 k= 1.74717117169304146332; Table[Length[Select[Range[Ceiling[n^k],Floor[(n+1)^k]], 
               PrimeQ]], {n,150}]
%Y A143935 A014085 (number of primes between n^2 and (n+1)^2)
%Y A143935 Sequence in context: A085035 A083023 A084359 this_sequence A008616 A097471 
               A025868
%Y A143935 Adjacent sequences: A143932 A143933 A143934 this_sequence A143936 A143937 
               A143938
%K A143935 nonn
%O A143935 1,1
%A A143935 T. D. Noe (noe(AT)sspectra.com), Sep 05 2008
%E A143935 Corrected a(15) from 1 to 0 Enoch Haga (Enokh(AT)comcast.net), Sep 24 
               2008
%E A143935 My intention was to include the endpoints of the range. Using k=log(127)/
               log(16), the endpoint for n=15 is exactly 127, which is prime. - 
               T. D. Noe (noe(AT)sspectra.com), Sep 25 2008