%I #8 Aug 18 2017 11:03:10

%S 2,17,43,89,257,283,359,593,599,1297,2213,2617,3391,3631,4129,4177,

%T 4721,6569,7561,8081,8233,9277,10343,10657,10729,11273,12197,13049,

%U 13463,14449,14561,15641,15881,16369,16921,17209,17657,19699,22067,24137

%N Primes of the form a^4 + b^3 with b>0.

%H Vincenzo Librandi, <a href="/A100271/b100271.txt">Table of n, a(n) for n = 1..1000</a>

%t lst={}; Do[p=a^4+b^3; If[p<50000&&PrimeQ[p], AppendTo[lst, p]], {a, 64}, {b, 256}]; Union[lst]

%o (PARI) list(lim)=my(v=List([2]),a4,t); lim\=1; for(a=1,sqrtnint(lim-1,4), a4=a^4; forstep(b=1+a%2,sqrtnint(lim-a4,3),2, if(isprime(t=a4+b^3), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Aug 18 2017

%Y Cf. A002645 (primes of the form a^4 + b^4), A028916 (primes of the form a^4 + b^2), A100291 (numbers of the form a^4 + b^3).

%K nonn

%O 1,1

%A _T. D. Noe_, Nov 18 2004