A100271 Primes of the form a^4 + b^3 with b>0.

2, 17, 43, 89, 257, 283, 359, 593, 599, 1297, 2213, 2617, 3391, 3631, 4129, 4177, 4721, 6569, 7561, 8081, 8233, 9277, 10343, 10657, 10729, 11273, 12197, 13049, 13463, 14449, 14561, 15641, 15881, 16369, 16921, 17209, 17657, 19699, 22067, 24137

Offset: 1

Author

T. D. Noe, Nov 18 2004

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

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).

Programs

Mathematica

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

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