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

1,48

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.

Links

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

Example

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

Prog

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

Crossrefs

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

Cf. A083844, A214452, A214454, A214455.

Sequence in context: A261226 A003108 A279223 * A209899 A111898 A279041

Adjacent sequences: A214953 A214954 A214955 * A214957 A214958 A214959

Keyword

nonn

Author

Henryk Dabrowski, Jul 30 2012

Status

approved