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%I #14 Jun 02 2020 12:21:43
%S 2,5,11,31,41,89,103,181,281,311,353,419,769,797,811,839,853,911,1091,
%T 1153,1201,1217,1249,1499,1621,1873,2081,2557,2999,3307,3533,3671,
%U 3881,3929,4289,5431,6131,6269,6491,6547,7001,7349,7583
%N Primes of the form floor(k^(3/2)) for some integer k.
%C While Piatetski-Shapiro proved that there are infinitely many primes of the form floor(n^e) with 1 < e < 12/11, it is not currently known if this sequence is infinite.
%H Charles R Greathouse IV, <a href="/A291139/b291139.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjecturally, a(n) ~ (1.5 n log n)^1.5 and there are ~ x^(2/3)/log x members of this sequence up to x. - _Charles R Greathouse IV_, Oct 14 2017
%e a(1) = floor(2^(3/2)) = floor(2.8...) = 2.
%e a(2) = floor(3^(3/2)) = floor(5.1...) = 5.
%e floor(4^(3/2)) = floor(8) = 8 is composite.
%e a(3) = floor(5^(3/2)) = floor(11.1) = 11.
%e floor(6^(3/2)) = floor(14.6...) = 14 is composite.
%e floor(7^(3/2)) = floor(18.5...) = 18 is composite.
%e floor(8^(3/2)) = floor(22.6...) = 22 is composite.
%e floor(9^(3/2)) = floor(27) = 27 is composite.
%e a(4) = floor(10^(3/2)) = floor(31.6) = 31.
%t Select[Floor[Range[1000]^(3/2)],PrimeQ] (* _Harvey P. Dale_, Jul 01 2019 *)
%o (PARI) list(lim)=my(v=List(),t); lim\=1; for(n=2,sqrtnint((lim+1)^2,3)-ispower(lim+1,3), if(isprime(t=sqrtint(n^3)), listput(v,t))); Vec(v)
%Y Cf. A200141.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Aug 18 2017
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