cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A215050 #33 Aug 11 2020 01:26:41
%S A215050 1,5,48,291,2194,17907,152447,1322985,11669082
%N A215050 Number of primes of the form 1 + b^16 for 1 < b < 10^n.
%C A215050 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).
%H A215050 Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/results.html">Status of the smallest base values yielding Generalized Fermat primes</a>
%H A215050 Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/stat.html">How many prime numbers appear in a sequence ?</a>
%H A215050 Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/papers/ccdgfpn.html">A Problem on the Conjecture Concerning the Distribution of Generalized Fermat Prime numbers (a new method for the search for large primes)</a>
%F A215050 a(n) = A214455(16*n) - 1.
%e A215050 a(1) = 1 because the only Fermat prime F_4(b) where b<10^1 is the prime 65537.
%t A215050 Table[Length[Select[Range[2,10^n-1]^16 + 1, PrimeQ]], {n, 5}] (* _T. D. Noe_, Aug 02 2012 *)
%t A215050 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 *)
%o A215050 (PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^16+1))
%Y A215050 Cf. A214455, A215047, A215048, A215049, A215051.
%K A215050 nonn,more
%O A215050 1,2
%A A215050 _Henryk Dabrowski_, Aug 01 2012
%E A215050 a(9) from _Kellen Shenton_, Aug 10 2020