# Seriously disagreement

Peter Pein petsie at dordos.net
Tue Sep 2 23:52:07 CEST 2008

```Hi Artur,

nice to read you again :)

I would not believe _any_ result of someone who thinks that 1 is prime....

With a naive bruteforce method I get (with Mathematica):
In[1]:= ((Count[2*#1^2 - 1, _?PrimeQ] & )[Range[10^#1]] & ) /@ Range[6]
Out[1]= {7, 45, 303, 2202, 17185, 141444}

which starts like your sequence does.

Cheers,
Peter

Artur schrieb:
> Dear Seqfans,
> On www page
> we can read that number of primes of the form 2x^2-1 for x equal or less
> than 10^n is
> 8, 84, 815, 7922, 77250, 759077, 7492588, 74198995, 736401956,
> 7319543971, 72834161467
> my result by Mathematica is
> 7,45,303,2202,17185,141444,1200975
> disagreement of first position we can eliminated if we agree that 1 is
> prime but what with rest ???
> Best wishes
> Artur
>
> %S A143835 7,45,303,2202,17185,141444,1200975
> %N A143835 a(n) = Number of n less or equal 10^n such than 2n^2-1 is prime
> %e A143835 a(1)=7 because are 7 different n ={2, 3, 4, 6, 7, 8, 10}
> equal or less than 10^1 where 2n^2-1 is prime = {7, 17, 31, 71, 97, 127,
> 199}
> %t A143835 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*)
> %Y A143835 A066436, A066049, A090686, A090684, A143826, A143827,
> A143828, A143829, A143830, A143831, A143832, A143833, A143834
> %K A143835 base,nonn
> %O A143835 1,1
> %A A143835 Artur Jasinski (grafix(AT)csl.pl), Sep 02 2008
>

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