|
%I #26 Sep 08 2022 08:46:13
%S 161004359399459161,171649260008631991,182294160617804821,
%T 192939061226977651,203583961836150481,214228862445323311,
%U 224873763054496141,235518663663668971,246163564272841801,256808464882014631,267453365491187461,278098266100360291,288743166709533121
%N a(n) = 161004359399459161 + (n-1)*10644900609172830.
%C The terms n = 1..26 are prime. This is the longest and largest sequence of primes in arithmetic progression, a(26)=427126874628779911, known as of August 10, 2015.
%H Jens Kruse Andersen, <a href="http://primerecords.dk/aprecords.htm#ap24">All known AP24 to AP26</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression#Largest_known_primes_in_AP">Largest known primes in AP</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 161004359399459161 + (n-1)*47715109*A002110(9).
%F G.f.: x*(161004359399459161 - 150359458790286331*x)/(1 - x)^2. [_Bruno Berselli_, Aug 23 2015]
%e a(26) = 161004359399459161 + 25*10644900609172830 = 427126874628779911 is prime.
%t Table[161004359399459161 + (n - 1) 10644900609172830, {n, 1, 20}] (* _Bruno Berselli_, Aug 23 2015 *)
%o (Magma) [161004359399459161+(n-1)*10644900609172830: n in [1..20]]; // _Bruno Berselli_, Aug 23 2015
%Y Cf. A002110, A204189, A260751.
%K nonn,easy
%O 1,1
%A _Marco Ripà_, Aug 10 2015
| 