A192320 Numbers k for which there are no prime numbers in the range (k-4*sqrt(sqrt(k)), k].

1, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 1360, 19657, 19658, 19659, 19660, 25522, 31451, 31452, 31453, 31454, 31455, 31456, 31457, 31458, 31459, 31460, 31461, 31462, 31463, 31464, 31465, 31466, 31467, 31468, 34116, 34117, 34118, 34119, 34120, 34121, 34122

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 27 2011

Keywords

• nonn

Comments

a(69) = 492226 is probably the last term. Any further terms must be greater than 1.5 * 10^18. [Charles R Greathouse IV, Jun 27 2011]

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..69

Crossrefs

Subsequence of A192231.

Cf. A000040, A001223, A005669.

Programs

Maple

isA192320 := proc(n) floor( n-4*root[4](n)) ; nextprime(%) > n ; end proc:
for n from 1 do if isA192320(n) then printf("%d,\n",n) ;end if; end do: # R. J. Mathar, Jun 29 2011

PARI

isA192320(n)=nextprime(floor(n+1-4*n^.25))>n \\ Charles R Greathouse IV, Jun 27 2011

Extensions

a(15) inserted, a(25) and a(34)-a(40) corrected by Charles R Greathouse IV, Jun 27 2011