A192390 - OEIS

%I #22 May 13 2013 01:49:40

%S 1,2,6,10,21

%N Numbers n such that number of primes in the range (2^n-sqrt(2^n), 2^n] is equal to number of primes in the range (2^n, 2^n+sqrt(2^n)].

%C a(6) > 60. Probably a finite sequence. [_Charles R Greathouse IV_, Jun 30 2011]

%e a(1)=1 because 2 in range (2^1-sqrt(1), 2^1]=(1, 2] and 3 in range (2^1, 2^1+sqrt(1)]=(2, 3].

%e a(3)=6 because 59, 61 in range (2^6-sqrt(2^6), 2^6]=(56, 64] and 67, 71 in range (2^6, 2^6+sqrt(2^6)]=(64, 72].

%e a(4)=10 because 997, 1009, 1013, 1019, 1021 in range (2^10-sqrt(2^10), 2^10]=(992, 1024] and 1031, 1033, 1039, 1049, 1051 in range (2^10, 2^10+sqrt(2^10)]=(1024, 1056].

%o (PARI) ct(a,b)=sum(k=floor(a)+1,b,isprime(k))

%o is(n)=ct(2^n-sqrt(2^n-.5), 2^n)==ct(2^n, 2^n+sqrt(2^n+.5)) \\ _Charles R Greathouse IV_, Jul 19 2011

%K nonn,more

%O 1,2

%A _Juri-Stepan Gerasimov_, Jun 29 2011