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A261140 a(n) = 3486107472997423 + (n-1)*371891575525470.

%I A261140 #35 Jul 27 2024 09:40:31
%S A261140 3486107472997423,3857999048522893,4229890624048363,4601782199573833,
%T A261140 4973673775099303,5345565350624773,5717456926150243,6089348501675713,
%U A261140 6461240077201183,6833131652726653,7205023228252123,7576914803777593,7948806379303063,8320697954828533
%N A261140 a(n) = 3486107472997423 + (n-1)*371891575525470.
%C A261140 The terms n = 1..26 are prime. This is the longest sequence of primes in arithmetic progression with smallest end, a(26)=12783396861134173, known as of August 10, 2015.
%H A261140 Colin Barker, <a href="/A261140/b261140.txt">Table of n, a(n) for n = 1..1000</a>
%H A261140 Jens Kruse Andersen, <a href="http://primerecords.dk/aprecords.htm#ap24">All known AP24 to AP26</a>.
%H A261140 Wikipedia, <a href="https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression#Largest_known_primes_in_AP">Largest known primes in AP</a>.
%H A261140 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A261140 a(n) = 3486107472997423 + (n-1)*1666981*A002110(9).
%F A261140 G.f.: -x*(3114215897471953*x-3486107472997423) / (x-1)^2. - _Colin Barker_, Aug 25 2015
%e A261140 a(26) = 3486107472997423 + 25*371891575525470 = 12783396861134173 is prime.
%t A261140 Table[3486107472997423 + (n - 1) 371891575525470, {n, 1, 20}]
%t A261140 LinearRecurrence[{2,-1},{3486107472997423,3857999048522893},20] (* _Harvey P. Dale_, May 14 2022 *)
%o A261140 (Magma) [3486107472997423+(n-1)*371891575525470: n in [1..20]];
%o A261140 (PARI) Vec(-x*(3114215897471953*x-3486107472997423)/(x-1)^2 + O(x^40)) \\ _Colin Barker_, Aug 25 2015
%Y A261140 Cf. A002110, A033188, A033290, A204189, A260751, A327760, A363980, A374949.
%K A261140 nonn,easy
%O A261140 1,1
%A A261140 _Marco Ripà_, Aug 10 2015