A261151 - OEIS

%I #20 Sep 08 2022 08:46:13

%S 11410337850553,11871247719973,12332157589393,12793067458813,

%T 13253977328233,13714887197653,14175797067073,14636706936493,

%U 15097616805913,15558526675333,16019436544753,16480346414173,16941256283593,17402166153013,17863076022433,18323985891853

%N a(n) = 11410337850553 + (n-1)*4609098694200.

%C The terms n = 1..22 are prime. This is the longest known sequence of 22 primes in arithmetic progression with minimal end known as of August 10, 2015.

%H Colin Barker, <a href="/A261151/b261151.txt">Table of n, a(n) for n = 1..1000</a>

%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) = 11410337850553 + (n-1)*475180*A002110(8).

%F G.f.: -x*(10949427981133*x-11410337850553) / (x-1)^2. - _Colin Barker_, Aug 25 2015

%e a(22) = 11410337850553 + 21*4609098694200 = 108201410428753 is prime.

%t Table[11410337850553 + (n - 1) 4609098694200, {n, 1, 20}]

%o (Sage) [11410337850553+(n-1)*4609098694200 for n in (1..20)]

%o (Magma) [11410337850553+(n-1)*4609098694200: n in [1..20]];

%o (PARI) Vec(-x*(10949427981133*x-11410337850553) / (x-1)^2 + O(x^40)) \\ _Colin Barker_, Aug 25 2015

%Y Cf. A005115, A002110, A204189.

%K nonn,easy

%O 1,1

%A _Marco Ripà_, Aug 10 2015