A282704 (Twice product of first n primes) - 1.

1, 3, 11, 59, 419, 4619, 60059, 1021019, 19399379, 446185739, 12939386459, 401120980259, 14841476269619, 608500527054419, 26165522663340059, 1229779565176982819, 65178316954380089459, 3845520700308425278139, 234576762718813941966539

Offset: 0

Author

N. J. A. Sloane, Feb 26 2017

Keywords

• nonn

Comments

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

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A070826, A282705.

Programs

Magma

[1] cat [2*&*PrimesUpTo(p)-1: p in PrimesUpTo(70)]; // Vincenzo Librandi, Feb 28 2017

Maple

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

Mathematica

Join[{1}, 2 Denominator[Accumulate[1/Prime[Range[20]] - 1]] - 1] (* Vincenzo Librandi, Feb 28 2017 *)
Join[{1},2*FoldList[Times,Prime[Range[20]]]-1] (* Harvey P. Dale, Oct 09 2017 *)

PARI

a(n)=2*prod(i=1,n,prime(i))-1 \\ Charles R Greathouse IV, Feb 28 2017