A346809 Primes of the form x^2 + y^8.

2, 5, 17, 37, 101, 197, 257, 281, 337, 401, 577, 617, 677, 881, 1097, 1217, 1297, 1481, 1601, 1777, 2281, 2657, 2857, 2917, 3137, 4357, 4481, 5297, 5477, 5881, 6577, 6661, 6961, 7057, 7237, 7481, 7717, 8101, 8161, 8537, 8677, 8837, 9281, 9697, 10457, 10657, 12037

Offset: 1

Author

Michel Marcus, Aug 05 2021

Keywords

• nonn

Comments

Merikoski proves that this sequence is infinite.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Jori Merikoski, Exceptional characters and prime numbers in sparse sets, arXiv:2108.01355 [math.NT], 2021.

Crossrefs

Cf. A002496 (a subsequence), A028916.

Programs

PARI

lista(lim)=my(v=List([2]), t); for(a=1, sqrtint(lim), forstep(b=a%2+1, sqrtnint(lim-a^2, 8), 2, t=a^2+b^8; if(isprime(t), listput(v, t)))); vecsort(Vec(v), , 8); \\ after A028916