A214956 Number of primes of the form x^32 + 1 less than 10^n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8

Offset: 1

Author

Henryk Dabrowski, Jul 30 2012

Keywords

• nonn

Comments

It is conjectured that there are infinitely many primes of the form x^32 + 1 (and thus this sequence never becomes constant), but this has not been proved.

Examples

			a(55) = 2 because the only primes of the form x^32 + 1 < 10^55 are the primes: 2, 185302018885184100000000000000000000000000000001.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..304 (n = 1..128 from Henryk Dabrowski)

Crossrefs

Cf. A006315 (k such that k^32+1 is prime).

Cf. A083844, A214452, A214454, A214455.

Programs

PARI

a(n) = sum(k=1, (10^n-1)^(1/32), isprime(k^32+1))