A243859 - OEIS

%I #18 Apr 12 2022 11:56:32

%S 7,133153,184039,356929,469363,982843,2154487,2552713,2686573,3378103,

%T 3847867,4270069,4341373,4564363,4584847,4964899,5366017,5600989,

%U 6185173,6592609,6595597,6629683,6768409,8232277,9028429,9964177,10009339,12107089,13266553,13600189

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

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

%H Abhiram R Devesh, <a href="/A243859/b243859.txt">Table of n, a(n) for n = 1..141</a>

%e 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 p := 2:

%p for  n from 1 do

%p     if isprime(p+4) and isprime(p^3+4) and isprime(p^5+4) and isprime(p^7+4) then

%p         print(p) ;

%p     end if;

%p     p := nextprime(p) ;

%p end do: # _R. J. Mathar_, Jun 13 2014

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

%o (Python)

%o import sympy.ntheory as snt

%o n=2

%o while n>1:

%o ....n1=n+4

%o ....n2=((n**3)+4)

%o ....n3=((n**5)+4)

%o ....n4=((n**7)+4)

%o ....##Check if n1 , n2, n3 and n4 are also primes.

%o ....if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n3)== True and snt.isprime(n4)== True:

%o ........print(n, n1, n2, n3, n4)

%o ....n=snt.nextprime(n)

%Y Cf. A023200, A243583, A243780.

%K nonn

%O 1,1

%A _Abhiram R Devesh_, Jun 12 2014