A350687 Primes of the form x^2 + (y^3 + z^3)^2 with x,y,z > 0.

5, 13, 29, 53, 97, 173, 181, 229, 257, 277, 281, 293, 337, 617, 733, 757, 809, 881, 953, 1009, 1093, 1097, 1217, 1229, 1237, 1289, 1373, 1409, 1481, 1549, 1709, 1777, 1801, 1873, 1901, 2017, 2029, 2153, 2213, 2281, 2381, 2521, 2633

Offset

1,1

Comments

Merikoski proved that there are infinitely many primes of this form.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Jori Merikoski, The polynomials X^2+(Y^2+1)^2 and X^2+(Y^3+Z^3)^2 also capture their primes, arXiv:2112.03617 [math.NT], 2021.

Prog

(PARI) listA003325(lim)=my(v=List()); lim\=1; for(x=1, sqrtnint(lim-1, 3), my(x3=x^3); for(y=1, min(sqrtnint(lim-x3, 3), x), listput(v, x3+y^3))); Set(v)
list(lim)=lim\=1; my(v=List(), u=apply(sqr, listA003325(sqrtint(lim-1)))); for(x=1, sqrtint(lim-1), my(x2=x^2); for(i=1, #u, my(t=x2+u[i]); if(t>lim, break); if(isprime(t), listput(v, t)))); Set(v)

Crossrefs

Subsequence of A002144.

Cf. A349900, A028916, A003325.

Sequence in context: A078370 A308464 A247903 * A240130 A005473 A086732

Adjacent sequences: A350684 A350685 A350686 * A350688 A350689 A350690

Keyword

nonn

Author

Charles R Greathouse IV, Jan 11 2022

Status

approved