A215050 Number of primes of the form 1 + b^16 for 1 < b < 10^n.

1, 5, 48, 291, 2194, 17907, 152447, 1322985, 11669082

Offset

1,2

Comments

Primes 1 + b^16 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.229464*li(10^n).

Links

Table of n, a(n) for n=1..9.

Yves Gallot, Status of the smallest base values yielding Generalized Fermat primes

Yves Gallot, How many prime numbers appear in a sequence ?

Yves Gallot, A Problem on the Conjecture Concerning the Distribution of Generalized Fermat Prime numbers (a new method for the search for large primes)

Formula

a(n) = A214455(16*n) - 1.

Example

a(1) = 1 because the only Fermat prime F_4(b) where b<10^1 is the prime 65537.

Mathematica

Table[Length[Select[Range[2, 10^n-1]^16 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)
Module[{nn=8, t}, t=Table[If[PrimeQ[n^16+1], 1, 0], {n, 2, 10^nn}]; Table[Total[ Take[t, 10^i-1]], {i, nn}]] (* Harvey P. Dale, Sep 14 2015 *)

Prog

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^16+1))

Crossrefs

Cf. A214455, A215047, A215048, A215049, A215051.

Sequence in context: A215543 A212111 A359969 * A268785 A268736 A247769

Adjacent sequences: A215047 A215048 A215049 * A215051 A215052 A215053

Keyword

nonn,more

Author

Henryk Dabrowski, Aug 01 2012

Extensions

a(9) from Kellen Shenton, Aug 10 2020

Status

approved