A214455 Number of primes of the form x^16 + 1 less than 10^n.

1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 5, 6, 6, 6, 6, 9, 11, 11, 12, 14, 17, 20, 26, 27, 30, 34, 42, 49, 53, 59, 64, 68, 80, 93, 101, 111, 129, 147, 169, 187, 212, 235, 264, 292, 329, 386, 427, 483, 544, 622

Offset: 1

Author

Henryk Dabrowski, Jul 18 2012

Keywords

• nonn

Comments

It is conjectured that there are infinitely many primes of the form x^16 + 1 (and thus this sequence never becomes constant), but this has not been proved.

Examples

			a(26) = 2 because the only primes or the form x^16 + 1 < 10^26 are the primes: 2, 65537.
		

Crossrefs

Cf. A083844, A214452, A214454.

Programs

PARI

a(n) = sum(k=1, (10^n-1)^(1/16), isprime(k^16+1))