A192454 Number of primes in the range [2^n-n, 2^n+n].

0, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 2, 3, 2, 1, 3, 5, 3, 6, 2, 5, 4, 3, 5, 2, 0, 2, 0, 2, 2, 5, 3, 3, 4, 1, 1, 4, 4, 2, 4, 2, 3, 4, 2, 4, 0, 2, 3, 1, 0, 2, 1, 3, 2, 2, 4, 3, 5, 2, 1, 1, 6, 1, 2, 4, 1, 3, 7, 4, 2, 3, 2, 1, 2, 5, 3, 4, 6, 3, 3, 2, 4, 5, 2, 5, 2, 7, 3, 1, 7, 4, 3, 2, 3, 2, 4, 5, 0, 5, 0, 2

Offset: 0

Author

Juri-Stepan Gerasimov, Jul 01 2011

Keywords

• nonn

Examples

			a(1) = 2 because two primes in the range [1^2-1, 1^2+1], a(2) = 3 because 2, 3 and 5 are in range [2^2-2, 2^2+2].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000290, A192931.

Programs

Maple

with(numtheory); f:=n->pi(2^n+n)-pi(2^n-n-1); [seq(f(n),n=0..20)];
# second Maple program:
a:= n-> add(`if`(isprime(t), 1, 0), t=2^n-n..2^n+n):
seq(a(n), n=0..100);  # Alois P. Heinz, Sep 13 2011

Mathematica

Table[PrimePi[2^n + n] - PrimePi[2^n - n - 1], {n, 0, 40}]

Extensions

Corrected with Maple program. - N. J. A. Sloane, Jul 11 2011

Corrected name and added terms up to a(40). - T. D. Noe, Jul 12 2011

More terms from Alois P. Heinz, Sep 13 2011