A347110 Primes p such that 2*p+1 and (2*p)^2+(2*p+1)^2 are also prime.

2, 11, 41, 281, 641, 761, 1451, 1481, 1811, 2741, 3821, 4211, 4481, 5441, 5501, 7121, 7691, 7901, 8111, 9791, 10061, 10331, 11171, 12011, 13451, 15401, 16001, 16421, 17351, 17981, 18041, 27281, 28961, 30851, 31151, 32561, 33941, 35111, 36191, 43391, 43691, 43721, 45131, 45641, 49331, 49811, 50411, 50591

Offset

1,1

Comments

All terms except 2 end in 1.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 41 is a term because 41, 2*41+1 = 83 and (2*41)^2+(2*41+1)^2 = 13613 are prime.

Maple

filter:= proc(p) isprime(p) and isprime(2*p+1) and isprime(8*p^2+4*p+1) end proc:
select(filter, [2, seq(i, i=3..100000, 2)]);

Mathematica

Select[Prime@ Range[5190], AllTrue[{# + 1, #^2 + (# + 1)^2}, PrimeQ] &[2 #] &] (* Michael De Vlieger, Aug 18 2021 *)

Prog

(Python)
from sympy import isprime, primerange
def ok(p): return isprime(2*p+1) and isprime((2*p)**2 + (2*p+1)**2)
print(list(filter(ok, primerange(1, 50592)))) # Michael S. Branicky, Aug 18 2021
(PARI) isok(p) = isprime(p) && isprime(2*p+1) && isprime(8*p^2+4*p+1); \\ Michel Marcus, Aug 18 2021

Crossrefs

Intersection of A005384 and A103776.

Sequence in context: A260267 A128241 A258937 * A225907 A107020 A160945

Adjacent sequences: A347107 A347108 A347109 * A347111 A347112 A347113

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 18 2021

Status

approved