A228115 First differences of A227693.

3, 21, 143, 1061, 8366, 68932, 585881, 5094722, 45074595, 404185377, 3663479699, 33498077106, 308548877876, 2859703657128, 26646019345842, 249434445759050, 2344494354096166, 22116172789221197, 209301155352811190, 1986521422431963549, 18904049485198437478, 180323870540071281301, 1723847795281971132487, 16512536418951055856540, 158463448213030472998711

Offset: 1

Author

Vladimir Pletser, Aug 10 2013

Keywords

• nonn

Comments

This sequence gives a good approximation of the number of primes with n digits (A006879); see (A228116).

Examples

			For n =1, A227693(1)- A227693(0) =4-1=3, where A227693(1)= round((F[3]( 1.016825…))^2)=4 with F[3](x) = x^2+1 and A227693(0)= round(F[1](x)) =1 with F[1](x)=1
		

References

• John H. Conway and R. K. Guy, The Book of Numbers, Copernicus, an imprint of Springer-Verlag, NY, 1996, page 144.

Links

• Vladimir Pletser, Table of n, a(n) for n = 1..500
• Eric Weisstein's World of Mathematics, Fibonacci Polynomial.

Crossrefs

Cf. A006879, A228111 - A228116

Formula

a(n)= A227693(n)- A227693(n-1)