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 A349327 Primes p such that 2*p^2 is a term of A179993. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MATHEMATICA q[n_] := AllTrue[{n, n^2 - 2, 2*n^2 - 1}, PrimeQ]; Select[Range, q] PROG (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 CROSSREFS 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 KEYWORD nonn AUTHOR Amiram Eldar, Nov 15 2021 STATUS approved

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Last modified March 30 23:40 EDT 2023. Contains 361623 sequences. (Running on oeis4.)