A282704 - OEIS

%I #17 Sep 08 2022 08:46:18

%S 1,3,11,59,419,4619,60059,1021019,19399379,446185739,12939386459,

%T 401120980259,14841476269619,608500527054419,26165522663340059,

%U 1229779565176982819,65178316954380089459,3845520700308425278139,234576762718813941966539

%N (Twice product of first n primes) - 1.

%C Used to prove there are infinitely many primes of the form 4k-1 (see A282705).

%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 147.

%H Vincenzo Librandi, <a href="/A282704/b282704.txt">Table of n, a(n) for n = 0..200</a>

%p f:=n->mul(ithprime(i),i=1..n); s1 := [seq(2*f(n)-1,n=0..20)];

%t Join[{1}, 2 Denominator[Accumulate[1/Prime[Range[20]] - 1]] - 1] (* _Vincenzo Librandi_, Feb 28 2017 *)

%t Join[{1},2*FoldList[Times,Prime[Range[20]]]-1] (* _Harvey P. Dale_, Oct 09 2017 *)

%o (Magma) [1] cat [2*&*PrimesUpTo(p)-1: p in PrimesUpTo(70)]; // _Vincenzo Librandi_, Feb 28 2017

%o (PARI) a(n)=2*prod(i=1,n,prime(i))-1 \\ _Charles R Greathouse IV_, Feb 28 2017

%Y Cf. A070826, A282705.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Feb 26 2017