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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 (list; graph; refs; listen; history; text; internal format)
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)]);

CROSSREFS

Intersection of A005384 and A052291.

Sequence in context: A038526 A082755 A042067 * A338262 A042579 A033090

Adjacent sequences:  A333800 A333801 A333802 * A333804 A333805 A333806

KEYWORD

nonn

AUTHOR

Robert Israel, Apr 05 2020

STATUS

approved

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Last modified May 12 02:23 EDT 2021. Contains 343808 sequences. (Running on oeis4.)