A283072 - OEIS

%I #20 Mar 06 2017 09:35:39

%S 2,2823521,5402681,6272737,7641961,11046193,11139761,15785213,

%T 17669153,20109377,25855177,28083953,37168961,37681297,40466033,

%U 41565049,42025793,42221269,42550577,42911753,48066173,52249657,64377449,71213257,76895761,77051053,82456481,85983349,89197877

%N Primes of the form x^2 + y^2 such that x^k + y^k is prime for each k = 4, 8, 16, and 32.

%H Charles R Greathouse IV, <a href="/A283072/b283072.txt">Table of n, a(n) for n = 1..3900</a>

%e Prime 5 = 2^2 + 1^2 is not a term since 641 divides 2^32 + 1^32.

%e Prime 7641961 = 2669^2 + 720^2 is a term since 2669^4 + 720^4, 2669^8 + 720^8, 2669^16 + 720^16, and 2669^32 + 720^32 are prime numbers.

%o (PARI) list(lim)=my(v=List([2]), t); for(a=1, sqrt(lim), forstep(b=1+a%2, min(a, sqrt(lim-a^2)), 2, if(isprime(t=a^2+b^2) && isprime(a^4+b^4) && isprime(a^8+b^8) && isprime(a^16+b^16) && isprime(a^32+b^32), listput(v, t)))); vecsort(Vec(v)) \\ after _Charles R Greathouse IV_ at A182313

%Y Subsequence of A182313.

%K nonn

%O 1,1

%A _Altug Alkan_ and _Thomas Ordowski_, Feb 28 2017