A192319 - OEIS

%I #14 Mar 04 2019 11:19:54

%S 1,1358,1359,1360,31464,31465,31466,31467,31468

%N Numbers k such that the half-open interval (k-5*sqrt(sqrt(k)), k] does not contain primes.

%C a(9) = 31468 is probably the last term. Any further terms must be greater than 1.5 * 10^18. [_Charles R Greathouse IV_, Jun 27 2011]

%p isA192319 := proc(n) phigh := n ; plow := ceil(n-5*root[4](n))-1 ; numtheory[pi](phigh)-numtheory[pi](plow) = 0 ; end proc:

%p for n from 1 do if isA192319(n) then print(n); end if; end do: # _R. J. Mathar_, Jul 10 2011

%o (PARI) isA192319(n)=nextprime(floor(n+1-5*n^.25))>n \\ _Charles R Greathouse IV_, Jun 27 2011

%Y Subsequence of A192320.

%Y Cf. A000040, A005669.

%K nonn,more

%O 1,2

%A _Juri-Stepan Gerasimov_, Jun 27 2011