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

%I A243859 #20 May 22 2025 10:21:38
%S A243859 7,133153,184039,356929,469363,982843,2154487,2552713,2686573,3378103,
%T A243859 3847867,4270069,4341373,4564363,4584847,4964899,5366017,5600989,
%U A243859 6185173,6592609,6595597,6629683,6768409,8232277,9028429,9964177,10009339,12107089,13266553,13600189
%N A243859 Primes p for which p^i + 4 is prime for i = 1, 3, 5 and 7.
%C A243859 This is a subsequence of A243780: Primes p for which p^i + 4 is prime for i = 1, 3 and 5.
%H A243859 Abhiram R Devesh, <a href="/A243859/b243859.txt">Table of n, a(n) for n = 1..141</a>
%e A243859 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).
%p A243859 p := 2:
%p A243859 for  n from 1 do
%p A243859     if isprime(p+4) and isprime(p^3+4) and isprime(p^5+4) and isprime(p^7+4) then
%p A243859         print(p) ;
%p A243859     end if;
%p A243859     p := nextprime(p) ;
%p A243859 end do: # _R. J. Mathar_, Jun 13 2014
%t A243859 Select[Prime[Range[900000]],AllTrue[#^{1,3,5,7}+4,PrimeQ]&] (* _Harvey P. Dale_, Apr 12 2022 *)
%o A243859 (Python)
%o A243859 import sympy.ntheory as snt
%o A243859 n=2
%o A243859 while n>1:
%o A243859     n1=n+4
%o A243859     n2=((n**3)+4)
%o A243859     n3=((n**5)+4)
%o A243859     n4=((n**7)+4)
%o A243859     ##Check if n1 , n2, n3 and n4 are also primes.
%o A243859     if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n3)== True and snt.isprime(n4)== True:
%o A243859         print(n, n1, n2, n3, n4)
%o A243859     n=snt.nextprime(n)
%Y A243859 Cf. A023200, A243583, A243780.
%K A243859 nonn
%O A243859 1,1
%A A243859 _Abhiram R Devesh_, Jun 12 2014