OFFSET
1,1
COMMENTS
The generalized Bunyakovsky conjecture implies there are infinitely many terms.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Mathematics StackExchange,Find all p such that p, 2p+1, 4p^2+1 are prime
EXAMPLE
a(3)=5 is a member because 5, 2*5+1=11 and 4*5^2+1= 101 are all prime.
MAPLE
filter:= proc(n)
isprime(n) and isprime(2*n+1) and isprime(4*n^2+1)
end proc:
select(filter, [2, 3, seq(i, i=5..10^5, 6)]);
MATHEMATICA
Select[Prime[Range[4000]], AllTrue[{2#+1, 4#^2+1}, PrimeQ]&] (* Harvey P. Dale, Sep 15 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Apr 05 2020
STATUS
approved