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A347165 Primes p such that 2*p-1 and (2*p-1)^2+(2*p)^2 are also prime. 1
3, 79, 379, 829, 1279, 2029, 3019, 3109, 3529, 3709, 5479, 5749, 6379, 6709, 7219, 7369, 8689, 11839, 12049, 13219, 13729, 14029, 14419, 15319, 15349, 16189, 17659, 18229, 18439, 20809, 24979, 25819, 26539, 28549, 30859, 32119, 32359, 32779, 33739, 34729, 37039, 38569, 39079, 39679, 44119, 44449 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Except for 3, all terms end in 9.

LINKS

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

EXAMPLE

a(3) = 379 is a term because 379, 2*379-1 = 757 and (2*379-1)^2+(2*379)^2 = 1147613 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, [3, seq(i, i=9..50000, 10)]);

PROG

(Python)

from sympy import isprime, primerange

def ok(p): return isprime(2*p-1) and isprime((2*p-1)**2 + (2*p)**2)

def aupto(limit): return list(filter(ok, primerange(2, limit+1)))

print(aupto(44450)) # Michael S. Branicky, Aug 20 2021

CROSSREFS

Cf. A347110.

Sequence in context: A222192 A236069 A064456 * A073176 A236574 A062660

Adjacent sequences:  A347162 A347163 A347164 * A347166 A347167 A347168

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Aug 20 2021

STATUS

approved

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Last modified October 1 04:31 EDT 2022. Contains 357134 sequences. (Running on oeis4.)