A192231 Numbers k without prime numbers in the range (k-3*sqrt(sqrt(k)), k].

1, 123, 124, 125, 126, 306, 330, 538, 539, 540, 904, 905, 906, 1147, 1148, 1149, 1150, 1346, 1347, 1348, 1349, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 1360, 1689, 1690, 1691, 1692, 1971, 1972, 2200, 2201

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 26 2011

Keywords

• nonn

Comments

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

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..934

Crossrefs

Subsequence of A192226.

Cf. A001223, A188817, A189025, A192926.

Programs

Mathematica

Select[Range[2000], PrimePi[# - 3Sqrt[Sqrt[#]]] == PrimePi[#] &] (* Alonso del Arte, Jun 27 2011 *)

PARI

isA192231(n)=nextprime(floor(n+1-3*n^.25))>n \\ Charles R Greathouse IV, Jun 27 2011

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

Extensions

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