A192226 -id:A192226 - cp's OEIS frontend

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

Juri-Stepan Gerasimov, Jun 26 2011

nonn

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

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

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

Subsequence of A192226.

Cf. A001223, A188817, A189025, A192926.

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

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

is(n)=for(k=0,sqrtnint(81*n-1,4),if(isprime(n-k), return(0))); 1 \\ Charles R Greathouse IV, Aug 26 2015

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

A192227 Number of primes in the range (n - 2*sqrt(sqrt(n)), n].

Original entry on oeis.org

0, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2011

nonn

a(n) is probably positive for all n > 191913030. - Charles R Greathouse IV, Jul 01 2011

Cf. A188817, A189025, A192226.

A192227 := proc(n) local nhi, nlo ; nhi := n ; nlo := floor( n-2*root[4](n)) ; numtheory[pi](nhi)-numtheory[pi](nlo) ; end proc; # R. J. Mathar, Jul 12 2011

Table[PrimePi[n]-PrimePi[n-2*Sqrt[Sqrt[n]]],{n,90}] (* Harvey P. Dale, Feb 24 2018 *)

Conjecturally, a(n) ~ 2*n^(1/4)/log n. - Charles R Greathouse IV, Jul 01 2011

cp's OEIS Frontend

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

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