login
Numbers n without prime numbers in the range (n-3*sqrt(sqrt(n)), n].
2

%I #23 Aug 26 2015 12:21:45

%S 1,123,124,125,126,306,330,538,539,540,904,905,906,1147,1148,1149,

%T 1150,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,

%U 1358,1359,1360,1689,1690,1691,1692,1971,1972,2200,2201

%N Numbers n without prime numbers in the range (n-3*sqrt(sqrt(n)), n].

%C a(934) = 20831532 is probably the last term. Any further terms must be greater than 1.5 * 10^18. - _Charles R Greathouse IV_, Jun 27 2011

%H Charles R Greathouse IV, <a href="/A192231/b192231.txt">Table of n, a(n) for n = 1..934</a>

%e a(2)=123 because (123-3*sqrt(sqrt(123)), 123]=(123-9,9907.., 123]=(113,0092.., 123].

%t Select[Range[2000], PrimePi[# - 3Sqrt[Sqrt[#]]] == PrimePi[#] &] (* _Alonso del Arte_, Jun 27 2011 *)

%o (PARI) isA192231(n)=nextprime(floor(n+1-3*n^.25))>n \\ _Charles R Greathouse IV_, Jun 27 2011

%o (PARI) is(n)=for(k=0,sqrtnint(81*n-1,4),if(isprime(n-k), return(0))); 1 \\ _Charles R Greathouse IV_, Aug 26 2015

%Y Subsequence of A192226.

%Y Cf. A001223, A188817, A189025, A192926.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Jun 26 2011

%E a(2) added by Alonso del Arte, Jun 27 2011