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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 September 24 04:42 EDT 2020. Contains 337317 sequences. (Running on oeis4.)