|
|
A282704
|
|
(Twice product of first n primes) - 1.
|
|
2
|
|
|
1, 3, 11, 59, 419, 4619, 60059, 1021019, 19399379, 446185739, 12939386459, 401120980259, 14841476269619, 608500527054419, 26165522663340059, 1229779565176982819, 65178316954380089459, 3845520700308425278139, 234576762718813941966539
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
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
|
|
|
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 *)
|
|
PROG
|
(Magma) [1] cat [2*&*PrimesUpTo(p)-1: p in PrimesUpTo(70)]; // Vincenzo Librandi, Feb 28 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|