A214454 Number of primes of the form x^8 + 1 less than 10^n.

1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 7, 8, 13, 15, 23, 29, 41, 52, 65, 84, 114, 149, 194, 257, 336, 431, 547, 686, 880, 1151, 1478, 1961, 2499, 3258, 4264, 5550, 7231, 9416, 12286, 16031, 20887, 27181, 35466, 46009, 60053, 78107, 102086, 133309, 174369, 227810

Offset: 1

Author

Henryk Dabrowski, Jul 18 2012

Keywords

• nonn

Comments

It is conjectured that there are infinitely many primes of the form x^8 + 1 (and thus this sequence never becomes constant), but this has not been proved.

Examples

			a(16) = 3 because the only primes of the form x^8 + 1 < 10^16 are the primes: 2, 257, 65537.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..90 (terms 1..72 from Henryk Dabrowski)

Crossrefs

Cf. A083844, A214452, A214455.

Programs

PARI

a(n) = sum(k=1,(10^n-1)^(1/8), isprime(k^8+1))

Extensions

More terms from Henryk Dabrowski, Jul 28 2012