A283072 Primes of the form x^2 + y^2 such that x^k + y^k is prime for each k = 4, 8, 16, and 32.
2, 2823521, 5402681, 6272737, 7641961, 11046193, 11139761, 15785213, 17669153, 20109377, 25855177, 28083953, 37168961, 37681297, 40466033, 41565049, 42025793, 42221269, 42550577, 42911753, 48066173, 52249657, 64377449, 71213257, 76895761, 77051053, 82456481, 85983349, 89197877
Offset: 1
Keywords
Examples
Prime 5 = 2^2 + 1^2 is not a term since 641 divides 2^32 + 1^32. 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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..3900
Crossrefs
Subsequence of A182313.
Programs
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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