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A333803
Primes p such that 2*p+1 and 4*p^2+1 are also prime.
1
2, 3, 5, 233, 653, 683, 1013, 1973, 2003, 2393, 2543, 2753, 3023, 3413, 5003, 5333, 7043, 7823, 8663, 9293, 10613, 13463, 13913, 14783, 15233, 15923, 16823, 18233, 20693, 20753, 21713, 21803, 22433, 27743, 27983, 29723, 30323, 30773, 31253, 31793, 32003, 33053, 33623, 33773, 34283, 36083, 37013
OFFSET
1,1
COMMENTS
The generalized Bunyakovsky conjecture implies there are infinitely many terms.
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
Intersection of A005384 and A052291.
Sequence in context: A038526 A082755 A042067 * A338262 A376605 A042579
KEYWORD
nonn
AUTHOR
Robert Israel, Apr 05 2020
STATUS
approved