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A349327
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Primes p such that 2*p^2 is a term of A179993.
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2
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2, 3, 7, 13, 43, 127, 211, 293, 743, 757, 797, 811, 1429, 1597, 1721, 2087, 2113, 2239, 2269, 2297, 2381, 2423, 2647, 3079, 3121, 3221, 3863, 4229, 4271, 4957, 5209, 5333, 5923, 6299, 6691, 7127, 7237, 7349, 7757, 7853, 8329, 8513, 8539, 8807, 9127, 9311, 9631, 9661
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OFFSET
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1,1
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COMMENTS
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The numbers of the form 2*p^2 where p is a term of this sequence are the only nonsquarefree terms of A179993.
Equivalently, primes p such that p^2 - 2 and 2*p^2 - 1 are also primes, or primes p such that p^2 - 2 is a term of A023204.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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EXAMPLE
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2 is a term since 2*2^2 = 8 = 1*8 = 2*4 is a term of A179993: 8 - 1 = 7 and 4 - 2 = 2 are both primes.
3 is a term since 2*3^2 = 18 = 1*18 = 2*9 = 3*6 is a term of A179993: 18 - 1 = 17, 9 - 2 = 7 and 6 - 3 = 3 are all primes.
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MATHEMATICA
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q[n_] := AllTrue[{n, n^2 - 2, 2*n^2 - 1}, PrimeQ]; Select[Range[10000], q]
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PROG
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(Python)
from itertools import islice
from sympy import isprime, nextprime
def A349327(): # generator of terms
n = 2
while True:
if isprime(n**2-2) and isprime (2*n**2-1): yield n
n = nextprime(n)
A349327_list = list(islice(A349327(), 20)) # Chai Wah Wu, Nov 15 2021
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CROSSREFS
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Cf. A013929, A023204, A179993.
Intersection of A062326 and A106483.
The prime terms of A225098.
Sequence in context: A096263 A007996 A206579 * A166945 A257393 A273814
Adjacent sequences: A349324 A349325 A349326 * A349328 A349329 A349330
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KEYWORD
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nonn
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AUTHOR
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Amiram Eldar, Nov 15 2021
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STATUS
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approved
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