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

1,1

Links

Table of n, a(n) for n=1..12.

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

Example

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}.

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*)

Crossrefs

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

Sequence in context: A219020 A280597 A301319 * A103719 A134437 A018927

Adjacent sequences: A143832 A143833 A143834 * A143836 A143837 A143838

Keyword

nonn

Author

Artur Jasinski, Sep 02 2008, Sep 04 2008

Extensions

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

Status

approved