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A242326
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Primes p for which p + 2, p^3 + 2 and p^5 + 2 are prime.
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2
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419, 2339, 14081, 45821, 46349, 51419, 56039, 68489, 70379, 108191, 112601, 115319, 131891, 132749, 256391, 267611, 278879, 314159, 328511, 342449, 361001, 385139, 424841, 433259, 470651, 489689, 519371, 573761, 664691, 691181, 694271
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OFFSET
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1,1
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COMMENTS
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Subsequence of A001359 and A048637.
All the terms in the sequence are congruent to 2 mod 3. This sequence is a subsequence of A240110.
Also, congruent to (11, 29) mod 30. - Zak Seidov, May 18 2014
Also, subsequence of A216976. - Michel Marcus, May 18 2014
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LINKS
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Abhiram R Devesh, Table of n, a(n) for n = 1..1000
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EXAMPLE
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419 is in the sequence because
p = 419 (prime),
p + 2 = 421 (prime),
p^3 + 2 = 73560061 (prime), and
p^5 + 2 = 12914277518101 (prime).
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MATHEMATICA
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Select[Prime[Range[10^5]], PrimeQ[# + 2]&& PrimeQ[#^3 + 2]&& PrimeQ[#^5 + 2] &] (* Vincenzo Librandi, May 11 2014 *)
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PROG
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(Python)
n=2
co=1
while n>1:
....n1=n+2
....n2=((n*n*n)+2)
....n3=((n*n*n*n*n)+2)
....##.Check if n1, n2 and n3 are also primes
....if pf.isp(n1)== True and pf.isp(n2)== True and pf.isp(n3)== True:
........print(n, " , " , n1, " , ", n2, " , ", n3)
....n=pf.nextp(n)
(Magma) [p: p in PrimesUpTo(10^6)| IsPrime(p+2) and IsPrime(p^3+2)and IsPrime(p^5+2)]; // Vincenzo Librandi, May 11 2014
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CROSSREFS
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Cf. A001359, A048637.
Sequence in context: A060230 A255097 A130737 * A298699 A187218 A239253
Adjacent sequences: A242323 A242324 A242325 * A242327 A242328 A242329
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KEYWORD
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nonn
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AUTHOR
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Abhiram R Devesh, May 10 2014
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STATUS
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approved
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