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 A242326 Primes p for which p + 2, p^3 + 2 and p^5 + 2 are prime. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Abhiram R Devesh, Table of n, a(n) for n = 1..1000 EXAMPLE 419 is in the sequence because p = 419 (prime), p + 2 = 421 (prime), p^3 + 2 = 73560061 (prime), and p^5 + 2 = 12914277518101 (prime). MATHEMATICA Select[Prime[Range[10^5]], PrimeQ[# + 2]&& PrimeQ[#^3 + 2]&& PrimeQ[#^5 + 2] &] (* Vincenzo Librandi, May 11 2014 *) PROG (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 CROSSREFS Cf. A001359, A048637. Sequence in context: A060230 A255097 A130737 * A298699 A187218 A239253 Adjacent sequences: A242323 A242324 A242325 * A242327 A242328 A242329 KEYWORD nonn AUTHOR Abhiram R Devesh, May 10 2014 STATUS approved

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Last modified March 25 13:03 EDT 2023. Contains 361521 sequences. (Running on oeis4.)