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

Author

Henryk Dabrowski, Aug 01 2012

Keywords

• nonn
• more

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).

Examples

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

Links

• 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)

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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

Extensions

a(9) from Kellen Shenton, Aug 10 2020