A143835 a(n) = Number of x <= 10^n such that 2x^2-1 is prime.

7, 45, 303, 2202, 17185, 141444, 1200975, 10448345, 92435171, 828797351, 7511268020, 68680339342

Offset: 1

Author

Artur Jasinski, Sep 02 2008, Sep 04 2008

Keywords

• nonn

Examples

			a(1) = 7 because are 7 different x ={2, 3, 4, 6, 7, 8, 10} <= 10^1 where 2x^2-1 is prime = {7, 17, 31, 71, 97, 127, 199}.
		

Links

• Bernhard Helmes, Prime sieving on the polynomial f(n)=2n^2-1.

Crossrefs

Cf. A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143832, A143833, A143834.

Programs

Mathematica

l = 0; p = 2; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], l = l + 1]; If[N[Log[x]/Log[10]] == Round[N[Log[x]/Log[10]]], Print[l]; AppendTo[a, l]], {x, 1, 10000000}]; a (*Artur Jasinski*)

Extensions

Added link and extended to agree with website. - Ray Chandler, Jun 30 2015