A242326 Primes p for which p + 2, p^3 + 2 and p^5 + 2 are prime.

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

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