A196671 The number of Chebyshev primes (of index 1) less than 10^n, (n=1,2,...).

0, 0, 42, 516, 4498, 414123

Offset: 1

Author

Michel Planat, Oct 05 2011

Keywords

• nonn

Comments

The Chebyshev primes (of index 1) are such odd primes that satisfy li[psi(p)]-li[psi(p-1)]<1 (sequence A196667), where li(x) is the logarithmic integral and psi(x) is the Chebyshev's psi function.

The present sequence lists the number of Chebyshev primes less than 10^n, (n=1,2,...).

The sequence suggests the density pi(x)/2 for the Chebyshev primes, where pi(x) is the density of primes.

Links

• M. Planat and P. Solé, Efficient prime counting and the Chebyshev primes arXiv:1109.6489 [math.NT]

Crossrefs

Cf. A196667.