A243859 Primes p for which p^i + 4 is prime for i = 1, 3, 5 and 7.

7, 133153, 184039, 356929, 469363, 982843, 2154487, 2552713, 2686573, 3378103, 3847867, 4270069, 4341373, 4564363, 4584847, 4964899, 5366017, 5600989, 6185173, 6592609, 6595597, 6629683, 6768409, 8232277, 9028429, 9964177, 10009339, 12107089, 13266553, 13600189

Offset

1,1

Comments

This is a subsequence of A243780: Primes p for which p^i + 4 is prime for i = 1, 3 and 5.

Links

Abhiram R Devesh, Table of n, a(n) for n = 1..141

Example

p=7 is in this sequence as p + 4 = 11 (prime), p^3 + 4 = 347 (prime), p^5 + 4 = 16811 (prime), and p^7 + 4 = 823547 (prime).

Maple

p := 2:
for  n from 1 do
    if isprime(p+4) and isprime(p^3+4) and isprime(p^5+4) and isprime(p^7+4) then
        print(p) ;
    end if;
    p := nextprime(p) ;
end do: # R. J. Mathar, Jun 13 2014

Mathematica

Select[Prime[Range[900000]], AllTrue[#^{1, 3, 5, 7}+4, PrimeQ]&] (* Harvey P. Dale, Apr 12 2022 *)

Prog

(Python)
import sympy.ntheory as snt
n=2
while n>1:
....n1=n+4
....n2=((n**3)+4)
....n3=((n**5)+4)
....n4=((n**7)+4)
....##Check if n1 , n2, n3 and n4 are also primes.
....if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n3)== True and snt.isprime(n4)== True:
........print(n, n1, n2, n3, n4)
....n=snt.nextprime(n)

Crossrefs

Cf. A023200, A243583, A243780.

Sequence in context: A090769 A013842 A247791 * A297059 A306256 A145322

Adjacent sequences: A243856 A243857 A243858 * A243860 A243861 A243862

Keyword

nonn

Author

Abhiram R Devesh, Jun 12 2014

Status

approved